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
Birkhäuser, Basel, 2007. ISBN: 978-3-7643-8267-4
Click here for
more information.
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
Birkhäuser, Basel, 2010. ISBN: 978-3-7643-8752-5
Click here for more information.
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.
Accepted for publication in
Linear Algebra and
its Applications.
(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.
Submitted for publication.
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.
Submitted for publication.
122.
A.C.M. Ran and M. Wojtylak:
Eigenvalues of rank one perturbations of
unstructured matrices.
Submitted for publication.
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,
To appear in European Journal
on Control 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.