17 citations · 50 across the 19 of their papers we have counts for
19 papers
A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: Invertibility and Riccati equations
G. J. Groenewald, S. ter Horst, J. Jaftha +1
This paper is a continuation of the work on unbounded Toeplitz-like operators $T_\Om$ with rational matrix symbol $\Om$ initiated in Groenewald et. al (Complex Anal. Oper. Theory 1…
A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: Fredholm characteristics
G. J. Groenewald, S. ter Horst, J. J. Jaftha +1
In a recent paper (Groenewald et al.\ {\em Complex Anal.\ Oper.\ Theory} \textbf{15:1} (2021)) we considered an unbounded Toeplitz-like operator generated by a rational matri…
Equivalence after extension and Schur coupling for Fredholm operators on Banach spaces
Sanne ter Horst, Niels Jakob Laustsen
Schur coupling (SC) and equivalence after extension (EAE) are important relations for bounded operators on Banach spaces. It has been known for 30 years that the former implies the…
A Hill-Pick matrix criteria for the Lyapunov order
Sanne ter Horst, Alma van der Merwe
The Lyapunov order appeared in the study of Nevanlinna-Pick interpolation for positive real odd functions with general (real) matrix points. For real or complex matrices and $B…
The Infinite-Dimensional Standard and Strict Bounded Real Lemmas in Continuous Time: The storage function approach
Joseph A. Ball, Sanne ter Horst, Mikael Kurula
The bounded real lemma (BRL) is a classical result in systems theory, which provides a linear matrix inequality criterium for dissipativity, via the Kalman-Yakubovich-Popov (KYP) i…
Equivalence after extension for compact operators on Banach spaces
Sanne ter Horst, Miek Messerschmidt, André C. M. Ran
In recent years the coincidence of the operator relations equivalence after extension and Schur coupling was settled for the Hilbert space case, by showing that equivalence after e…
State space formulas for a suboptimal rational Leech problem II: Parametrization of all solutions
A. E. Frazho, S. ter Horst, M. A. Kaashoek
For the strictly positive case (the suboptimal case), given stable rational matrix functions and , the set of all solutions to the Leech problem associated wi…
State space formulas for a suboptimal rational Leech problem I: Maximum entropy solution
A. E. Frazho, S. ter Horst, M. A. Kaashoek
For the strictly positive case (the suboptimal case) the maximum entropy solution to the Leech problem and , with $…
State space formulas for stable rational matrix solutions of a Leech problem
A. E. Frazho, S. ter Horst, M. A. Kaashoek
Given stable rational matrix functions and , a procedure is presented to compute a stable rational matrix solution to the Leech problem associated with and , that…
A pre-order on positive real operators and its invariance under linear fractional transformations
S. ter Horst
A pre-order and equivalence relation on the class of positive real Hilbert space operators are introduced, in correspondence with similar relations for contraction operators define…
A pre-order and an equivalence relation on Schur class functions and their invariance under linear fractional transformations
S. ter Horst
Motivated by work of Yu.L. Shmul'yan a pre-order and an equivalence relation on the set of operator-valued Schur class functions are introduced and the behavior of Redheffer linear…
Bounded Real Lemma and structured singular value versus diagonal scaling: the free noncommutative setting
Joseph A. Ball, Gilbert J. Groenewald, Sanne ter Horst
The structured singular value was introduced independently by Doyle and Safanov as a tool for analyzing robustness of system stability and performance in the presence of struct…
Coupling and relaxed commutant lifting
A. E. Frazho, S. ter Horst, M. A. Kaashoek
A Redheffer type description of the set of all contractive solutions to the relaxed commutant lifting problem is given. The description involves a set of Schur class functions whic…
Optimal solutions to matrix-valued Nehari problems and related limit theorems
A. E. Frazho, S. ter Horst, M. A. Kaashoek
In a 1990 paper Helton and Young showed that under certain conditions the optimal solution of the Nehari problem corresponding to a finite rank Hankel operator with scalar entries…
Robust control, multidimensional systems and multivariable Nevanlinna-Pick interpolation
J. A. Ball, S. ter Horst
The connection between the standard -problem in control theory and Nevanlinna-Pick interpolation in operator theory was established in the 1980s, and has led to a fruitfu…
Redheffer representations and relaxed commutant lifting
S. ter Horst
It is well known that the solutions of a (relaxed) commutant lifting problem can be described via a linear fractional representation of the Redheffer type. The coefficients of such…
A time-variant norm constrained interpolation problem arising from relaxed commutant lifting
A. E. Frazho, S. ter Horst, M. A. Kaashoek
A time-variant analogue of an interpolation problem equivalent to the relaxed commutant lifting problem is introduced and studied. In a somewhat less general form the problem alrea…
A constrained Nevanlinna-Pick interpolation problem for matrix-valued functions
J. A. Ball, V. Bolotnikov, S. ter Horst
Recent results of Davidson-Paulsen-Raghupathi-Singh give necessary and sufficient conditions for the existence of a solution to the Nevanlinna-Pick interpolation problem on the uni…
Multivariable generalizations of the Schur class: positive kernel characterization and transfer function realization
Joseph A. Ball, Animikh Biswas, Quanlei Fang +1
The operator-valued Schur-class is defined to be the set of holomorphic functions mapping the unit disk into the space of contraction operators between two Hilbert spaces. Ther…