# André C.M. Ran: List of Publications Arranged by Topics

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## Spectral and J-spectral Factorization

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

## Other Rational Matrix Functions with Symmetries

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

## Interpolation of Rational Matrix Functions

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

## Factorization of Rational Matrix Functions

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.

## Riccati Equations

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

## Other Matrix Equations

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.

## Stability of Invariant Subspaces of Matrices

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

## Stability of Invariant Subspaces of Matrices with Symmetries

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)

## Matrices in Indefinite Inner Product Spaces

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.

## Polar Decompositions of Matrices in Indefinite Inner Product Spaces

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.

## Eigenvalues of rank one perturbations of matrices

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.

## Systems and Control

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.
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.

## Transport Equation

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

## Operator Theory

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.

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.

## Miscellaneous

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