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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 \Pik.
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.
Accepted for publication in Linear Algebra and its Applications.
(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.
Submitted for publication.
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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--ECC2011.
Pia L. Kempker, André C.M. Ran, Jan H. van Schuppen:
Controllability and observability
of coordinated linear systems.
Submitted for publication.
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,
To appear in
European Journal on Control
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 Theory47 (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.
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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