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- Spectral and J-spectral Factorization
- Other Rational Matrix Functions with Symmetries
- Interpolation of Rational Matrix Functions
- Factorization of Rational Matrix Functions
- Riccati Equations
- Other Matrix Equations
- Stability of Invariant Subspaces of Matrices
- Stability of Invariant Subspaces of Matrices with Symmetries
- Matrices in Indefinite Inner Product Spaces
- Polar Decompositions of Matrices in Indefinite Inner Product Spaces
- Eigenvalues of rank one perturbations of matrices
- Systems and Control
- Transport Equation
- Operator Theory
- Miscellaneous

BOOKS

H. Bart, I. Gohberg, M.A. Kaashoek and A.C.M. Ran:
*A state space
approach to canonical factorization with applications.*

Operator Theory
Advances and Applications, Vol 200. Birkhäuser, Basel, 2010.

ISBN 978-
3-7643-8752-5

REFEREED RESEARCH PAPERS

Minimal factorization of selfadjoint rational
matrix functions.

*Integral Equations and Operator Theory*
5(1982), 850-869.

(See also Rapport nr. 173, Wiskundig
Seminarium, VU Amsterdam.)

A.C.M. Ran and L. Rodman:

Stability of invariant maximal semidefinite
subspaces II.
Applications:
self-adjoint rational matrix functions,
algebraic Riccati
equations.

*Linear Algebra and its Applications*
63(1984),133-173

M.A. Kaashoek and A.C.M. Ran:

Symmetric Wiener-Hopf factorization and
realization.

In: * Constructive methods of Wiener-Hopf
factorization*
(eds. I. Gohberg, M.A. Kaashoek), OT 21,
Birkhäuser, Basel etc.,
(1986), 373-409

A.C.M. Ran and L. Rodman:

Stable real invariant semidefinite subspaces
and stable factorizations
of symmetric rational matrix functions.

*Linear and Multilinear Algebra*
22(1987),25-55

A.C.M. Ran and L. Rodman:

Stable invariant Lagrangian subspaces:
factorization of symmetric
rational matrix functions and other
applications.

* Linear Algebra and its Applications*,
137/138(1990), 575-620

A.C.M. Ran and L. Rodman:

On symmetric factorizations of rational matrix
functions.

* Linear and Multilinear Algebra*
29(1991), 243-261

A.C.M. Ran and L. Rodman:

Factorization of matrix polynomials with
symmetries.

* SIAM Journal on Matrix Analysis and
Applications*
15(1994), 845-864

abstract

See also: IMA Preprint series no. 993.

A.C.M. Ran:

Minimal square spectral factors.

* Systems & Control Letters*
24(1995), 307-316

See also: Rapport nr. WS-418, Faculteit
Wiskunde en Informatica, VU Amsterdam

A.C.M. Ran and P. Zizler:

On selfadjoint matrix polynomials with
constant signature.

* Linear Algebra and its Applications* 259
(1997), 133-153

L. Lerer and A.C.M. Ran:

J-spectral and J-inner/outer
factorizations for a class of
matrix polynomials.

*
Integral Equations and Operator Theory*
29 (1997), 23-51

M.A. Petersen and A.C.M. Ran:

Minimal square spectral factors of positive
semidefinite
rational matrix functions.

* SIAM J. Matrix Analysis and
Applications* 22 (2001), 1222-1244
paper

I. Karelin, L. Lerer and A.C.M. Ran:

J-symmetric factorizations and algebraic
Riccati equations.

* Proceedings IWOTA 1998,
OT-series 124 (2001), 319-360*

M.A. Petersen and A.C.M. Ran:

Minimal nonsquare spectral factors.

* Linear Algebra and its Applications* 351-352 (2002), 553-565
preprint
or
you can find the paper here via Science Direct

M.A. Petersen and A.C.M. Ran:

Minimal nonsquare spectral factors via
factorizations of unitary functions.

* Linear Algebra and its Applications* 351-352 (2002), 567-583
preprint
or
you can find the paper here via Science Direct

M.A. Petersen and A.C.M. Ran:

Minimal Nonsquare $J$-Spectral Factorization, Generalized
Bezoutians and
Common Zeros for Rational Matrix Functions.

* Integral Equations and Operator Theory* 47 (2003),
197-216
preprint .

L.Lerer, M.A. Petersen and A.C.M. Ran:

Existence of Minimal Nonsquare $J$-Symmetric Factorizations
for Self-Adjoint Rational Matrix Functions.

* Linear Algebra and its Applications* 379 (2004), 159-178
preprint

A.C.M. Ran:

Necessary and sufficient conditions for existence of
J-spectral factorization for para-Hermitian rational matrix functions.

*Automatica 39 * (2003), 1935-1939
preprint

OTHER PUBLICATIONS

M.A. Petersen and A.C.M. Ran:

Symmetric nonsquare factorization of selfadjoint rational
matrix functions
and algebraic Riccati inequalities,

Proceedings of MTNS 2002
pdf-file

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REFEREED RESEARCH PAPERS

A.C.M. Ran and L. Rodman:

Semidefinite perturbations of analytic
hermitian matrix functions.

* Integral Equations and Operator Theory
*
12(1989), 739-745

I. Gohberg, M.A. Kaashoek and A.C.M. Ran:

Factorizations of and extensions to
J-unitary rational matrix
functions on the unit circle.

* Integral Equations and Operator Theory*
15(1992), 262-300

A.C.M. Ran and L. Rodman:

Generalized canonical factorization of matrix
and operator
functions with definite Hermitian part.

* Integral Equations and Operator Theory*
15(1992), 673-696

A.C.M. Ran, L. Rodman and J.E. Rubin:

Direct complements of invariant Lagrangian
subspaces and minimal
factorizations of real skew-symmetric rational
matrix functions.

* Linear Algebra and its Applications*
180(1993), 61-94

I. Gohberg and A.C.M. Ran:

On pseudo-canonical factorization of rational
matrix functions.

* Indagationes Mathematica* N.S. 4(1993),
51-63

A.C.M. Ran, L. Rodman and D. Temme:

Stability of pseudo-spectral factorizations.

In:
* Operator Theory and Analysis,
The M.A. Kaashoek Anniversary Volume*, OT 122
(eds. H. Bart, I. Gohberg, A.C.M. Ran),
Birkhäuser Verlag, Basel, 2001, 359-383

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REFEREED RESEARCH PAPERS

J.A. Ball and A.C.M. Ran:

Global inverse spectral problems for rational
matrix valued functions.

* Linear Algebra and its Applications*
86(1987), 237-282;

J.A. Ball and A.C.M. Ran:

Local inverse spectral problems for rational
matrix valued functions.

* Integral Equations and Operator Theory*
10(1987), 349-415

J.A. Ball, N. Cohen and A.C.M. Ran:

Inverse spectral problems for regular improper
rational matrix functions.

In: * Topics in Interpolation Theory of
Rational Matrix-valued
Functions*, OT-33, Birkhäuser, Basel etc.,
(1988), 123-173

I. Gohberg, M.A. Kaashoek and A.C.M. Ran:

Interpolation problems for rational matrix
functions with incomplete
data and Wiener-Hopf factorization.

In: * Topics in Interpolation Theory of
Rational Matrix-valued
Functions*, OT-33, Birkhäuser, Basel etc.,
(1988), 73-108

I. Gohberg, M.A. Kaashoek and A.C.M. Ran:

Partial pole and zero displacement by cascade
connection.

* SIAM Journal on Matrix Analysis and
Applications *,
10(1989), 316-325

I. Gohberg, M.A. Kaashoek and A.C.M. Ran:

Regular rational matrix functions with
prescribed null and pole data
except at infinity.

* Linear Algebra and its Applications*
137/138(1990), 387-412

I. Gohberg, M.A. Kaashoek and A.C.M. Ran:

Matrix polynomials with prescribed zero
structure in the finite complex plane.

In: * Topics in Matrix and Operator Theory*
(eds. H. Bart, I. Gohberg, M.A. Kaashoek)
OT 50, Birkhäuser, Basel etc., 1991,
241-266

A.C.M. Ran and L. Rodman:

Laurent interpolation for rational matrix
functions and a local factorization principle.

* Journal of Mathematical Analysis and
Applications* 164(1992), 524-541

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BOOKS

H. Bart, I. Gohberg, M.A. Kaashoek and A.C.M. Ran :

*
Factorization of Matrix and Operator Functions: The State Space
Method.
*
Series: Operator Theory: Advances and Applications
Subseries: Linear Operators and Linear Systems , Vol. 178
Birkhäuser, Basel, 2007. ISBN: 978-3-7643-8267-4
Click
here for more information.

REFEREED RESEARCH PAPERS

C.L. Prather and A.C.M. Ran:

A Hadamard factorization theorem for entire
matrix valued functions.

In: * Operator Theory and Systems* (eds.
H. Bart, I. Gohberg,
M.A. Kaashoek) OT 19, Birkhäuser, Basel
etc., (1986), 3 59-372

J.A. Ball and A.C.M. Ran:

Left versus right canonical Wiener-Hopf
factorization.

In: * Constructive
methods of Wiener-Hopf factorization* (eds. I.
Gohberg, M .A. Kaashoek)
OT 21, Birkhäuser, Basel etc., (1986), 9-38;

C.L. Prather and A.C.M. Ran:

Factorization of a class of meromorphic matrix
valued functions.

* Journal of Mathematical Analysis and
Applications* 127(1987),413-422

I. Gohberg, M.A. Kaashoek and A.C.M. Ran:

Interpolation problems for rational matrix
functions with incomplete
data and Wiener-Hopf factorization.

In: * Topics in Interpolation Theory of
Rational Matrix-valued
Functions*, OT-33, Birkhäuser, Basel etc.,
(1988), 73-108

M.A. Kaashoek, A.C.M. Ran and L.Rodman:

Local minimal factorizations of rational
matrix functions in terms
of null and pole data: formulas for factors.

*
Integral Equations and Operator Theory*
16(1993), 98-130

H. Bart, I. Gohberg, M.A. Kaashoek and A.C.M. Ran :

Schur Complements and State Space Realizations.

*Linear Algebra and its Applications*
399 (2005), 203-224.

A.E. Frazho, M.A. Kaashoek and A.C.M. Ran:

The non-symmetric discrete algebraic
Riccati equation and canonical factorization of rational matrix
functions on the unit circle.

*Integral Equations and Operator Theory.* 66 (2010), 215--229.

A.E. Frazho, M.A. Kaashoek and A.C.M. Ran:

Right invertible multiplication operators and stable rational matrix solutions to an associate Bezout equation,
I. the least squares solution.
*
Integral Equations and Operator Theory*
70 (2011), no. 3, 395–-418.

A.E. Frazho, M.A. Kaashoek and A.C.M. Ran:

Right invertible multiplication operators and
stable rational matrix solutions to an associate
Bezout equation, II: Description of all solutions.

Accepted for publication in *Operators and Matrices*.

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REFEREED RESEARCH PAPERS

A.C.M. Ran and L. Rodman:

Stability of invariant maximal semidefinite
subspaces II.
Applications:
self-adjoint rational matrix functions,
algebraic Riccati
equations.

*Linear Algebra and its Applications*
63(1984),133-173

P. Lancaster, A.C.M. Ran and L. Rodman:

Hermitian solutions of the discrete algebraic
Riccati equation.
*International Journal of Control*
44(1986), 777-802

P. Lancaster, A.C.M. Ran and L. Rodman:

An existence and monotonicity theorem for the
discrete algebraic Riccati equation.

* Linear and Multilinear Algebra* 20(1987),
353-361

A.C.M. Ran and R. Vreugdenhil:

Existence and comparison theorems for
algebraic Riccati equations
for continuous- and discrete time systems.

* Linear Algebra and its Applications*
99(1988), 63-83

A.C.M. Ran and L. Rodman:

On parameter dependence of solutions of
algebraic Riccati equations

* Mathematics of Control, Signals and
Systems*
1(1988), 269-284

A.C.M. Ran and L. Rodman:

Stable solutions of real algebraic Riccati
equations.

* SIAM Journal of Control and
Optimization*
30(1992), 63-81

A.C.M. Ran:

Unitary solutions of a class of algebraic
Riccati equations and
factorization.

* Linear Algebra and its Applications*
162-164(1992), 521-540

A.C.M. Ran and L. Rodman:

Stable Hermitian solutions of discrete
algebraic Riccati
equations.

* Mathematics of Control Signals and
Systems*
5(1992), 165-193

J.C. Engwerda, A.C.M. Ran and A.L. Rijkeboer:

Necessary and sufficient conditions for the
existence of a positive
solution of the matrix equation $X+ A^*
X^{-1}A =I$.

* Linear Algebra and its Applications *
184(1993), 255-275

A.C.M. Ran and L. Rodman:

Rate of stability of solutions of matrix
polynomial and quadratic
equations.

* Integral Equations and Operator Theory*
27 (1997), 71-102

H. Langer, A.C.M. Ran and D. Temme:

Nonnegative solutions of algebraic Riccati
equations.
* Linear Algebra and its Applications* 261
(1997), 317-352

I. Karelin, L. Lerer and A.C.M. Ran:

J-symmetric factorizations and algebraic
Riccati equations.

* Proceedings IWOTA 1998, OT 124, 319-360
*

H. Langer, A.C.M. Ran and B. van de Rotten:

Invariant Subspaces of infinite dimensional
Hamiltonians
and solutions of the corresponding Riccati
equations.

*
Linear Operators and Matrices,
The Peter Lancaster Anniversary Volume,
Operator Theory: Advances and Applications
*
130, 2001, 235-254
preprint

C.V.M. van der Mee and A.C.M. Ran:

Perturbation Results for Exponentially Dichotomous Operators
on General Banach Spaces.

*Journal of Functional Analysis* 210 (2004), 193-213
preprint

C.V.M. van der Mee and A.C.M. Ran:

Additive and Multiplicative Perturbations of Exponentially
Dichotomous Operators on General Banach Spaces

*Proceedings IWOTA 2003*
Operator Theory: Advances and Applications 160 (2005), 413-424
preprint

P. Bubak, C.V.M. van der Mee and A.C.M. Ran:

Approximation of Solutions of Riccati Equations.

Accepted for publication in
*SIAM J. Control and Opt.* 44 (2005), 1419-1435
preprint

A.E. Frazho, M.A. Kaashoek and A.C.M. Ran:

The non-symmetric discrete algebraic
Riccati equation and canonical factorization of rational matrix
functions on the unit circle.

*Integral Equations and Operator Theory.* 66 (2010), 215--229.

L. Lerer and A.C.M. Ran:

The discrete algebraic Riccati equation and Hermitian block Toeplitz matrices.

Submitted for publication.

EXPOSITORY AND SURVEY PAPERS

A.C.M. Ran and L.Rodman:

The algebraic matrix Riccati equation.

In: * Topics in Operator Theory,
Networks and Systems* (eds. H.Dym, I.Gohberg),
OT 12, Birkhäuser,
Basel etc. (1984), 351-381

OTHER PUBLICATIONS

A.C.M. Ran and L.Rodman:

Hermitian solutions of the discrete algebraic
Riccati equation.

In: * Workshop on the Riccati equation in
control, systems and
signals; Lecture Notes*, Sergio Bittanti ed.,
Pitagora Editrice, Bologna (1989), 93-94

A.C.M. Ran and L.Rodman:

Robust solution of algebraic Riccati equations.

* Proc. of American Control Conference*
(1990), 3058-3059

A.C.M. Ran and L.Rodman:

Discrete algebraic Riccati equations:
perturbations and stability of solutions.

* Proc. of International Symposium on
Circuits and Systems*
(1990), 1197-1198;

A.C.M. Ran and L.Rodman:

Perturbation analysis of algebraic matrix
Riccati equations.

* Proc. of the 29-th Control and Decision
Conference* (1990)

A.C.M. Ran and L.Rodman:

Rate of Stability of Hermitian Solutions of
Algebraic Riccati Equations.

* Proceedings of the 5-th SIAM conference
on Applied Linear Algebra * (1994), 3-6

H. Langer, A.C.M. Ran and D. Temme:

Inertia of Hermitian Solutions of the Algebraic Riccati Equations.

* Proceedings of the European Control
Conference*, 1997 (CD-Rom)

A.C.M. Ran:

Two theorems on the discrete algebraic Riccati
equation.

Rapport nr. WS-508 Wiskunde en Informatica,
Vrije Universiteit Amsterdam,1998
preprint

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REFEREED RESEARCH PAPERS

J.C. Engwerda, A.C.M. Ran and A.L. Rijkeboer:

Necessary and sufficient conditions for the
existence of a positive
solution of the matrix equation $X+ A^*
X^{-1}A =I$.

* Linear Algebra and its Applications *
184(1993), 255-275

A.C.M. Ran and S.M. El-Sayed:

On an iteration method for solving a class of
nonlinear matrix equations

* SIAM J. Matrix Analysis and
Applications* 23 (2001) 632-645
ps-file

A.C.M. Ran and M.C.B. Reurings:

On the Nonlinear Matrix Equation
X+A^{*} F(X)A=Q:
Solutions and Perturbation Theory.

*Linear Algebra and its Applications* 346 (2002), 15-26
preprint
Full text via ScienceDirect

A.C.M. Ran and M.C.B. Reurings:

The symmetric linear matrix equation.

*Electronic Journal of Linear Algebra* 9 (2002), 93-107
preprint
Web site for ELA

A.C.M. Ran and M.C.B. Reurings:

A fixed point theorem in partially ordered sets
and some applications to matrix equations.

*Proceedings of the AMS* 132 (2004), 1435-1443
preprint.

A.C.M. Ran and M.C.B. Reurings:

A nonlinear matrix equation connected to interpolation
theory.

*Linear Algebra and its Applications * 379 (2004), 289-302
preprint.

L. Lerer and A.C.M. Ran:

A new inertia theorem for Stein equations,
inertia of invertible hermitian block Toeplitz matrices and matrix
orthogonal polynomials.

*Integral Equations and Operator Theory* 47 (2003),
339-360
preprint .

A.C.M. Ran, M.C.B. Reurings and L. Rodman:

A perturbation analysis for nonlinear selfadjoint operator equations.

*SIAM J. Matrix Anal. Appl.* 28 (2006), no. 1, 89--104

A.C.M. Ran and L. Rodman:

Ranges of Sylvester maps and a minimal rank problem.

*Electronic Lin. Alg.* 20 (2010), pages 126--135.

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REFEREED RESEARCH PAPERS

A.C.M. Ran and L. Roozemond:

On strong $\alpha $-stability of invariant
subspaces of matrices.

In: * The Gohberg anniversary collection
*,
(eds. H. Dym, S. Goldberg, M.A. Kaashoek, P.
Lancaster),
OT-40, Birkhäuser, Basel etc.,
1989, 427-435

A.C.M. Ran, L. Rodman and A.L. Rubin:

Stability index of invariant subspaces of
matrices.

* Linear and Multilinear Algebra*
36(1993), 27-39

A.C.M. Ran and L. Rodman:

The rate of convergence of real invariant
subspaces.

* Linear Algebra and its Applications*
207(1994), 197-224

EXPOSITORY AND SURVEY PAPERS

A.C.M. Ran and L. Rodman:

On stability of invariant subspaces of
matrices.

* American Mathematical Monthly* 97(1990),
809-823

A.C.M. Ran and L. Rodman:

A Class of Robustness Problems in Matrix
Analysis.

in the proceedings of
the workshop in
honor of the 60th birthday of H. Dym.
(OT 134, 2002), 337-383
preprint

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REFEREED RESEARCH PAPERS

A.C.M. Ran and L. Rodman:

Stability of neutral invariant subspaces in
indefinite inner products
and stable symmetric factorizations.

*Integral Equations and Operator Theory*
6(1983), 536 -571

A.C.M. Ran and L. Rodman:

Stability of invariant maximal semidefinite
subspaces I.

*Linear Algebra and its Applications*
62(1984), 51-86

A.C.M. Ran and L. Rodman:

Stability of invariant maximal semidefinite
subspaces II.
Applications:
self-adjoint rational matrix functions,
algebraic Riccati
equations.

*Linear Algebra and its Applications*
63(1984),133-173

A.C.M. Ran and L. Rodman:

Stability of solutions of the operator
differential equation in
transport theory.

*Integral Equations and Operator Theory*
8(1985), 75- 118;

Erratum, ibid, 894.

A.C.M. Ran and L. Rodman:

Stable real invariant semidefinite subspaces
and stable factorizations
of symmetric rational matrix functions.

*Linear and Multilinear Algebra*
22(1987),25-55

A.C.M. Ran and L. Rodman:

Stability of invariant Lagrangian subspaces
I.

In: * Topics in Operator Theory, Constantin
Apostol Memorial Issue*,
OT 32, Birkhäuser, Basel etc.,
(1988),181-218

A.C.M. Ran and L. Rodman:

Stability of invariant Lagrangian subspaces
II.

In:
* The Gohberg anniversary collection*,
(eds. H. Dym, S. Goldberg, M.A. Kaashoek, P.
Lancaster),
OT-40, Birkhäuser, Basel etc.,
1989, 391-425

A.C.M. Ran and L. Rodman:

Stable invariant Lagrangian subspaces:
factorization of symmetric
rational matrix functions and other
applications.

* Linear Algebra and its Applications*,
137/138(1990), 575-620

A.C.M. Ran and L. Rodman:

Rate of stability of solutions of matrix
polynomial and quadratic
equations.

* Integral Equations and Operator Theory*
27 (1997), 71-102

A.C.M. Ran, L. Rodman and D. Temme:

Stability of pseudo-spectral factorizations.

In:
* Operator Theory and Analysis,
The M.A. Kaashoek Anniversary Volume*, OT 122
(eds. H. Bart, I. Gohberg, A.C.M. Ran),
Birkhäuser Verlag, Basel, 2001, 359-383

A.C.M. Ran and L. Rodman:

On the Index of Conditional Stability of Stable Invariant
Lagrangian
Subspaces.

*SIAM J. Matrix Anal. Appl.}* 29 (2007), 1181-1190.

Chr. Mehl, V. Mehrmann, A.C.M. Ran and L. Rodman:

Perturbation analysis of Lagrangian invariant subspaces of
symplectic
matrices.

* Linear and Multilinear Algebra}*. 57 (2009), 141-184.

EXPOSITORY AND SURVEY PAPERS

A.C.M. Ran and L. Rodman:

A Class of Robustness Problems in Matrix
Analysis,

in the proceedings of
the workshop in
honor of the 60th birthday of H. Dym.
(OT 134, 2002), 337-383
preprint

See also: Stability of invariant subspaces of
matrices with applications.

Rapport nr. WS-488, 1997.

OTHER PUBLICATIONS

A.C.M. Ran and L. Rodman:

Rate of stability of symmetric
factorizations.

* Proceedings of the European Control
Conference * 1997 (CD-rom)

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REFEREED RESEARCH PAPERS

A.C.M. Ran and F. Uhlig:

A note on a new description of invariant
maximal nonnegative subspaces
in an indefinite inner product space.

*Linear Algebra and its Applications*
71(1985), 273-274

A.C.M. Ran and D. Temme:

Dissipative matrices and
Invariant Maximal Semidefinite Subspaces.

* Linear Algebra and its Applications*
212/213(1994), 169-214

C.V.M. van der Mee, A.C.M. Ran and L. Rodman:

Classes of plus-matrices in finite dimensional
indefinite scalar product spaces.

* Integral Equations and Operator Theory
(Krein-volume)*; 30 (1998), 432-451

Chr. Mehl, A.C.M. Ran and L. Rodman:

Semidefinite invariant subspaces: degenerate inner products.

*Proceedings IWOTA 2002*
Operator Theory: Advances and Applications 149 (2004), 475--494
preprint

Chr. Mehl, A.C.M. Ran and L. Rodman:

Hyponormal matrices and semidefinite invariant subspaces in
indefinite inner products.

* Electronic Journal of Linear Algebra.
* 11 (2004), 192-204 preprint

Chr. Mehl, A.C.M. Ran and L. Rodman:

Invariant maximal positive subspaces and polar decompositions.

*Integral Equations and Operator Theory* 56 (2006), no. 1, 83--91.

D. Alpay, A.C.M. Ran and L. Rodman:

Basic Classes of Matrices with respect to Quaternionic
Indefinite Inner Product Spaces.

* Linear Algebra and its Applications * 416 (2006), 242-269.

J.H. Fourie, G.J. Groenewald and A.C.M. Ran:

Positive real matrices in indefinite inner product
spaces and invariant maximal semi definite subspaces.

* Linear Algebra and its Applications * 424 (2007), 346-370.

Chr. Mehl, A.C.M. Ran and L. Rodman:

Extension to maximal semidefinite invariant subspaces for
hyponormal matrices in indefinite inner products.

* Linear Algebra and its Applications * 421 (2007), 110-116.

J.S. Kes and A.C.M. Ran:

On the relation between $XX^{\left[*\right]}$ and
$X^{\left[*\right]}X$ in an indefinite inner product space.

* Operators and Matrices* 1 (2007), 181-197.

L. Lerer, I. Margulis, and A.C.M. Ran:

Inertia theorems for infinite dimensional operators.

*Operators and Matrices}* 2 (2008), 153-166.

A.C.M. Ran and M.~Wojtylak:

Analysis of spectral points of the operators $T^{[*]}T$ and $TT^{[*]}$ in a Krein space.

*Integral Equations and Operator Theory.* 63 (2009), 263-280.

A.C.M. Ran and M.~Wojtylak:

The pair of operators $T^{[*]}T$ and $TT^{[*]}$; J--dilations and
canonical forms.
*
Integral Equations and Operator Theory.* 68 (2010) 313--335.

F. Philipp, A.C.M. Ran and M. Wojtylak:

Local definitizability of
$TT^{[*]}$ and $T^{[*]}T$.

*
Integral Equations and Operator Theory*. 71 (2011), 491--508.

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REFEREED RESEARCH PAPERS

Y. Bolshakov, C.V.M. van der Mee, B.
Reichstein, A.C.M. Ran and L. Rodman:

Polar decompositions in finite dimensional
indefinite scalar product
spaces: special cases and applications.

In: * Recent Developments in Operator
Theory and its Applications*,
OT 87 (I. Gohberg, P. Lancaster, P.N.
Shivakumar, eds.)
Birkhäuser, Basel, 1996, 61-94

Erratum in
* Integral Equations and Operator Theory*
27 (1997), 497-501.

Y. Bolshakov, C.V.M. van der Mee, B.
Reichstein, A.C.M. Ran and L. Rodman:

Extensions of isometries in finite dimensional
indefinite scalar product spaces.

* SIAM Journal Matrix Analysis and
Applications*
18(1997), 752-774
paper

Y. Bolshakov, C.V.M. van der Mee, B.
Reichstein, A.C.M. Ran and L. Rodman:

Polar decompositions in finite dimensional
indefinite scalar product spaces: general theory.

* Linear Algebra and its Applications* 261
(1997), 91-141

C.V.M. van der Mee, A.C.M. Ran and L.
Rodman:

Stability of selfadjoint square roots and
polar
decompositions in indefinite scalar product
spaces.

* Linear Algebra and its Applications*;
302-303 (1999), 77-104
(here you can find the
paper)

C.V.M. van der Mee, A.C.M. Ran and L.
Rodman:

Stability of polar decompositions.

* Mat. Glasnik* 35 (2000), 137-148
(paper)

C.V.M. van der Mee, A.C.M. Ran and L.
Rodman:

Real Hamiltonian Polar Decompositions.

* SIAM J. Matrix Analysis and
Applications * 22 (2001), 1263-1273
paper

C.V.M. van der Mee, A.C.M. Ran and L. Rodman:

Polar Decompositions and Related Classes of Operators in
Spaces \Pi_{k}.

* Integral Equations and Operator Theory*
44 (2002), 50-70
preprint

Chr. Mehl, A.C.M. Ran and L. Rodman:

Polar decomposition of normal operators in indefinite inner
product spaces.

* Proceedings of third Workshop on Indefinite Inner Products
*
to appear in the OT-series
preprint

Chr. Mehl, A.C.M. Ran and L. Rodman:

Invariant maximal positive subspaces and polar decompositions.

*Integral Equations and Operator Theory* 56 (2006), no. 1, 83--91.

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Chr. Mehl, V. Mehrmann, A.C.M. Ran and L. Rodman:

Eigenvalue perturbation theory of structured matrices
under generic structured rank one perturbations.
*
Linear Algebra and its Applications*, 435 (2011), 687--716.

(Matheon, DFG Research Center
*Mathematics for key technologies* in Berlin, TU Berlin report no. 673)

C. Mehl, V. Mehrmann, A.C.M. Ran, L. Rodman:

Perturbation theory of selfadjoint matrices and sign characteristics
under generic structured rank one perturbations.

*Linear Algebra and its Applications* 436 (2012), 4027-4042..

(Matheon, DFG Research Center
*Mathematics for key technologies* in Berlin, TU Berlin report
no. 675.)

C. Mehl, V. Mehrmann, A.C.M. Ran, L. Rodman:

Jordan forms of real and complex matrices under rank one perturbations.

Submitted for publication.

A.C.M. Ran and M. Wojtylak:

Eigenvalues of rank one perturbations of unstructured matrices.

* Linear Algebra and its Applications* 437 (2012) 589–-600.

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BOOKS

Chr. Heij, A.C.M. Ran and F. van Schagen:

*Introduction to Mathematical Systems Theory:
Linear Systems, Identification and Control.*

Birkhäuser, Basel, 2006.
ISBN 3-7643-7548-5

REFEREED RESEARCH PAPERS

J.A. Ball and A.C.M. Ran:

Hankel norm approximation of rational matrix
functions in terms of their realization.

In: * Modelling, Identification and Robust
Control* (eds.
C. Byrnes, A. Lindquist), North Holland,
Amsterdam etc.,(1986), 285-296

J.A. Ball and A.C.M. Ran:

Optimal Hankel-norm model reduction and
Wiener-Hopf factorization I:
the canonical case.

* SIAM Journal of Control and Optimization*
25(1987), 362-382

J.A. Ball and A.C.M. Ran:

Optimal Hankel-norm model reduction and
Wiener-Hopf factorization II:
the non-canonical case.

* Integral Equations and Operator Theory*
10(1987), 416-436

J.A. Ball and A.C.M. Ran:

Hankel-norm approximation of real symmetric
rational matrix functions.

* Systems & Control Letters* 9(1987),
105-115

A.C.M. Ran:

Hankel-norm approximation for infinite
dimensional systems and
Wiener-Hopf factorization.

In: * Modelling, Robustness and Sensitivity
Reduction in Control Systems*
(ed. R.F. Curtain), Springer Verlag, Berlin
etc., (1987), 57-69

A.C.M. Ran:

State space formulas for a model matching
problem.

* Systems & Control Letters *
12(1989), 17-21

R.F. Curtain and A.C.M. Ran:

Explicit formulas for Hankel norm
approximations of infinite-dimensional
systems.

* Integral Equations and Operator Theory
*
12(1989), 455-469

A.C.M. Ran and H.L. Trentelman:

The regular free-endpoint linear quadratic
problem with indefinite cost
in discrete time.

* SIAM Journal on Matrix Analysis and
Applications* 14(1993), 776-797

M.A. Kaashoek, C.V.M. van der Mee and A.C.M.
Ran:

Weighting operator patterns of
Pritchard-Salamon realizations.

* Integral Equations and Operator Theory*
27 (1997), 48-70

M.A. Kaashoek and A.C.M. Ran:

Norm bounds for Volterra integral operators and
time varying linear systems with finite horizon.

In: * Operator Theory and its Applications
(Langer sixtieth birthday volume)*, OT 106
(eds. A. Dijksma, I. Gohberg, M.A. Kaashoek and R. Mennicken),
1998, 275-290

M.A. Kaashoek, C.V.M. van der Mee and A.C.M.
Ran:

Factorization of transfer functions of
Pritchard-Salamon systems.

* Mathematische Nachrichten*; 196 (1998),
71-102

H. Langer, A.C.M. Ran and B. van de Rotten:

Invariant Subspaces of infinite dimensional
Hamiltonians
and solutions of the corresponding Riccati
equations.

*
Linear Operators and Matrices,
The Peter Lancaster Anniversary Volume,
Operator Theory: Advances and Applications
*
130, 2001, 235-254
preprint

C.V.M. van der Mee and A.C.M. Ran:

Perturbation Results for Exponentially Dichotomous Operators
on General Banach Spaces.

*Journal of Functional Analysis* 210 (2004), 193-213
preprint

C.V.M. van der Mee and A.C.M. Ran:

Additive and Multiplicative Perturbations of Exponentially
Dichotomous Operators on General Banach Spaces

*Proceedings IWOTA 2003*
Operator Theory: Advances and Applications 160 (2005), 411-422
preprint

P. Bubak, C.V.M. van der Mee and A.C.M. Ran:

Approximation of Solutions of Riccati Equations.

Accepted for publication in
*SIAM J. Control and Opt.* 44 (2005), 1419-1435
preprint

Peter Dickinson, Joost Hulshof, Andr\'e Ran, Majid Salmani, Martijn Zaal:

Optimal Flood Control.

Submitted for publication.

A.C.M. Ran and J.H. van Schuppen:

Control for coordination of linear systems,

*Proceedings of MTNS 2008*, 2008. CD-ROM only.

P. Kempker, A.C.M. Ran and J.H. van Schuppen:

Construction of a coordinator for coordinated linear systems,

*Proceedings of ECC 2009*, 2009.

Pia L. Kempker, André C.M. Ran, Jan H. van Schuppen:

A Formation Flying Algorithm for Autonomous Underwater Vehicles.

*Proceedings of CDC--ECC*2011.

Pia L. Kempker, André C.M. Ran, Jan H. van Schuppen:

Controllability and observability
of coordinated linear systems.

* Linear Algebra and its Applications* 437 (2012) 589–-600.

EXPOSITORY AND SURVEY PAPERS

A.C.M. Ran:

An overview of Hankel norm model reduction.

In: * SVD and Signal Processing,
Algorithms, Applications and
Architectures*, (ed. Ed.F.Deprettere), North
Holland, Amsterdam etc. (1988), 149-159

Jan H. van Schuppen, Olivier Boutin, Pia L. Kempker, Jan Komenda, Tomás Masopust,
Nicola Pambakian, André C.M. Ran:

Control of Distributed Systems
- Tutorial and Overview,

*European Journal on Control* 17 (2011), 579--602.
Special issue for CDC.ECC.2011.

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REFEREED RESEARCH PAPERS

A.C.M. Ran and L. Rodman:

Stability of solutions of the operator
differential equation in
transport theory.

*Integral Equations and Operator Theory*
8(1985), 75- 118;

Erratum, ibid, 894.

A.C.M. Ran and L. Rodman:

A boundary value problem that arises from
transport theory.

* Journal of Mathematical Analysis and
Applications*
130(1988), 200-222

C.V.M. van der Mee, A.C.M. Ran and L. Rodman:

Stability of stationary transport equations with accretive collision operators.

* Journal of Functional Analysis* 174 (2000), 478-512
paper

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REFEREED RESEARCH PAPERS

M.A. Kaashoek and A.C.M. Ran:

Norm bounds for Volterra integral operators and
time varying linear systems with finite horizon.

In: * Operator Theory and its Applications
(Langer sixtieth birthday volume)*, OT 106
(eds. A. Dijksma, I. Gohberg, M.A. Kaashoek and R. Mennicken),
1998, 275-290

M.A. Petersen and A.C.M. Ran:

LU- versus UL-Factorization of Integral Operators with
Semi-Separable Kernel.

*Integral Equations and Operator Theory* 50 (2004), 549-558

preprint.

C.V.M. van der Mee and A.C.M. Ran:

Perturbation Results for Exponentially Dichotomous Operators
on General Banach Spaces.

*Journal of Functional Analysis* 210 (2004), 193--213
preprint

C.V.M. van der Mee and A.C.M. Ran:

Additive and Multiplicative Perturbations of Exponentially
Dichotomous Operators on General Banach Spaces

*Proceedings IWOTA 2003*
Operator Theory: Advances and Applications 160 (2005), 411-422
preprint

L. Lerer and A.C.M. Ran:

A new inertia theorem for Stein equations,
inertia of invertible hermitian block Toeplitz matrices and matrix
orthogonal polynomials.

*Integral Equations and Operator Theory*47 (2003),
339-360
preprint .

G.J. Groenewald, M.A. Petersen and A.C.M. Ran:

Characterization of
Integral Operators with Semi-Separable Kernel with Symmetries.

*Journal of Functional Analysis*
219 (2005), 255-284 paper .

L. Lerer, I. Margulis, and A.C.M. Ran:

Inertia theorems for infinite dimensional operators.

*Operators and Matrices* 2 (2008), 153-166.

A.E. Frazho, M.A. Kaashoek and A.C.M. Ran:

Right invertible multiplication operators and stable rational matrix solutions to an associate Bezout equation,
I. the least squares solution.
*
Integral Equations and Operator Theory*
70 (2011), no. 3, 395–-418.

A.E. Frazho, M.A. Kaashoek and A.C.M. Ran:

Right invertible multiplication operators and
stable rational matrix solutions to an associate
Bezout equation, II: Description of all solutions.

Accepted for publication in *Operators and Matrices*.

A.C.M. Ran and A. Ser\'eny:

The finite section method for infinite Vandermonde matrices.

To appear.

OTHER PUBLICATIONS

A.C.M. Ran:

A note on canonical upper-lower factorization
for a class of input-output operators of the form
I plus a strict contraction.

Rapport nr. WS-467, Faculteit Wiskunde en
Informatica, VU Amsterdam, 1996
preprint

M.A. Kaashoek and A.C.M. Ran:

A note on Toeplitz operators with unimodular symbol.
preprint

G.J. Groenewald, M.A. Petersen and A.C.M. Ran:

Lower-Upper and Upper-Lower Factorization of Integral Operators
with Semi-Separable Kernel and Symmetries. preprint.

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REFEREED RESEARCH PAPERS

D. Farkas and A.C.M. Ran:

Space group theoretical analysis of grain
boundaries in ordered alloys.

*Physica Status Solida A* 93(1986), 45-55;

J. van Mill and A.C.M. Ran:

On a generalization of Lyapounov's
Theorem.

* Indagationes Mathematica*
N.S. 7(2), (1996), 227-242

See also: Rapport nr. WS-431, Faculteit
Wiskunde en Informatica, VU Amsterdam

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