# Publications of A.C.M. Ran

## Recent Publications

### 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

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
A Maple worksheets for section 11.6 is available here , a Maple worksheet for Section 12.5 is available here.

H. Bart, I. Gohberg, M.A. Kaashoek and A.C.M. Ran:
A State Space Approach to Canonical Factorization with Applications.
Series: Operator Theory: Advances and Applications
Subseries: Linear Operators and Linear Systems , Vol. 200

### Papers, reports etc.

Below papers from 1998 onwards are listed in chronological order. For a complete overview of my publications that is listed according to topic see this list.

64. Classes of plus-matrices in finite dimensional indefinite scalar product spaces;
Integral Equations and Operator Theory (Krein-volume); 30 (1998), 432-451;
with C.V.M. van der Mee and L. Rodman.

65. Norm bounds for Volterra integral operators and time varying linear systems with finite horizon;
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;
with M.A. Kaashoek.

66. Factorization of transfer functions of Pritchard-Salamon systems;
Mathematische Nachrichten; 196 (1998), 71-102,
with M.A. Kaashoek and C.V.M. van der Mee.

67. Stability of selfadjoint square roots and polar decompositions in indefinite scalar product spaces;
Linear Algebra and its Applications; 302-303 (1999), 77-104,
with C.V.M. van der Mee and L. Rodman.

68. Stability of polar decompositions;
Mat. Glasnik; 35 (2000), 137-148.
with C.V.M. van der Mee and L. Rodman.

69. Stability of stationary transport equations with accretive collision operators;
Journal of Functional Analysis, 174 (2000), 478-512,
with C.V.M. van der Mee and L. Rodman. paper

70. 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;
with L. Rodman and D. Temme.

71. Minimal square spectral factors of positive semidefinite rational matrix functions;
SIAM J. Matrix Analysis and Appl. 22 (2001), 1222-1244
with M.A. Petersen. paper

72. J-symmetric factorizations and algebraic Riccati equations;
Proceedings IWOTA 1998, OT 124 (eds. A. Dijksma, M.A. Kaashoek, A.C.M. Ran), Birkhäuser Verlag, Basel, 2001, 319-360;
with I. Karelin and L. Lerer.

73. Real Hamiltonian Polar Decompositions;
SIAM J. Matrix Analysis and Appl. 22 (2001), 1263-1273
with C.V.M. van der Mee and L. Rodman paper

74. On an iteration method for solving a class of nonlinear matrix equations;
SIAM J. Matrix Analysis and Appl.;23 (2001) 632-645
with S.M. El-Sayed. ps-file

75. Minimal nonsquare spectral factors;
Linear Algebra and its Applications 351-352 (2002), 553-565
with M.A. Petersen. ps-file

76. 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
with H. Langer and B. van de Rotten. ps-file

77. Minimal nonsquare spectral factors via factorizations of unitary functions;
Linear Algebra and its Applications 351-352 (2002), 567-583
with M.A. Petersen. ps-file

78. A Class of Robustness Problems in Matrix Analysis.
in the proceedings of the workshop in honor of the 60th birthday of H. Dym, Operator Theory: Advances and Applications, 134, 337-383
with L. Rodman. ps-file

79. On the Nonlinear Matrix Equation X+A*F(X)A=Q: Solutions and Perturbation Theory;
Linear Algebra and its Applications 346 (2002) 15-26
with M.C.B. Reurings. ps-file

80. Polar Decompositions and Related Classes of Operators in Spaces \Pik;
Integral Equations and Operator Theory 44 (2002), 50-70,
with C.V.M. van der Mee and L. Rodman.

81. The symmetric linear matrix equation;
Electronic Journal of linear algebra 9 (2002), 93-107 ps-file Web site for ELA
with M.C.B. Reurings.

82. Minimal Nonsquare $J$-Spectral Factorization, Generalized Bezoutians and Common Zeros for Rational Matrix Functions.
Integral Equations and Operator Theory 47 (2003), 197-216
ps-file with M.A. Petersen.

83. LU- versus UL-Factorization of Integral Operators with Semi-Separable Kernel.
Integral Equations and Operator Theory 50 (2004), 549-558
ps-file with M.A. Petersen.

84. A fixed point theorem in partially ordered sets and some applications to matrix equations.
Proceedings of the American Mathematical Society 132 (2004), 1435-1443
ps-file with M.C.B. Reurings.

85. A nonlinear matrix equation connected to interpolation theory.
Linear Algebra and its Applications 379 (2004), 289-302
ps-file with M.C.B. Reurings.

86. Existence of Minimal Nonsquare $J$-Symmetric Factorizations for Self-Adjoint Rational Matrix Functions.
Linear Algebra and its Applications 379 (2004), 159-178
with L. Lerer and M.A. Petersen. ps-file

87. Semidefinite invariant subspaces: degenerate inner products.
Proceedings IWOTA 2002, Operator Theory: Advances and Applications 149 (2004), 475--494
with Chr. Mehl and L. Rodman. ps-file

88. Perturbation Results for Exponentially Dichotomous Operators on General Banach Spaces.
Journal of Functional Analysis 201 (2004), 193--213
with C.V.M. van der Mee. ps-file

89. 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

90. 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

91. 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 ps-file

92. 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 .

93. P. Bubak, C.V.M. van der Mee and A.C.M. Ran:
Approximation of Solutions of Riccati Equations.
SIAM J. Control and Opt. 44, (2005), 1419-1435. preprint

94. 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, OT-series 162, (2006) 277-292. preprint

95. 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

96. 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

97. 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.

98. 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

99. 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.

100. 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.
Submitted for publication.

101. 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.

102. 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.

103. 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.

104. 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.

105. 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.

106. 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.

107. L. Lerer, I. Margulis, and A.C.M. Ran:
Inertia theorems for infinite dimensional operators.
Operators and Matrices 2 (2008), 153-166.

108. 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.

109. 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.

110. 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 The- ory. 66 (2010), 215-229.

111. A.C.M. Ran and L. Rodman:
Ranges of Sylvester maps and a minimal rank problem.
Electronic Lin. Alg. 20 (2010), 126-135.

112. 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.

113. 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)

114. 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.)

115. 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.

116. L. Lerer and A.C.M. Ran:
The discrete algebraic Riccati equation and Hermitian block Toeplitz matrices.
In: A Panorama of Modern Operator Theory and Related Topics The Israel Gohberg Memorial Volum ( eds. Dym, H.; Kaashoek, M.A.; Lancaster, P.; Langer, H.; Lerer, L. ) OT, Volume 218, (2012), 495-512.

117. 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.

118. C. Mehl, V. Mehrmann, A.C.M. Ran, L. Rodman:
Jordan forms of real and complex matrices under rank one perturbations.
Submitted for publication.

119. Peter Dickinson, Joost Hulshof, Andre Ran, Majid Salmani, Martijn Zaal:
Optimal Flood Control.
Submitted for publication.

120. 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. Operators and Matrices

121. Pia L. Kempker, Andre C.M. Ran, Jan H. van Schuppen:
Controllability and observability of coordinated linear systems.
Linear Algebra and its Applications 437 (2012) 589–-600.

122. A.C.M. Ran and M. Wojtylak:
Eigenvalues of rank one perturbations of unstructured matrices.
Linear Algebra and its Applications 437 (2012) 589–-600.

123. Jan H. van Schuppen, Olivier Boutin, Pia L. Kempker, Jan Komenda, Tomas Masopust, Nicola Pambakian, Andre C.M. Ran:
Control of Distributed Systems - Tutorial and Overview,
European Journal on Control 17 (2011), 579--602. Special issue for CDC.ECC.2011.

124. A.C.M. Ran and J.H. van Schuppen:
Control for coordination of linear systems,
Proceedings of MTNS 2008, 2008. CD-ROM only.

125. P. Kempker, A.C.M. Ran and J.H. van Schuppen:
Construction of a coordinator for coordinated linear systems,
Proceedings of ECC 2009, 2009.

126. Pia L. Kempker, Andre C.M. Ran, Jan H. van Schuppen:
A Formation Flying Algorithm for Autonomous Underwater Vehicles.
Proc. CDC- ECC 2011.

127. A.C.M. Ran and A. Ser\'eny:
The finite section method for infinite Vandermonde matrices.
Indagationes Mathematicae