249 research outputs found
State space formulas for a suboptimal rational Leech problem I: Maximum entropy solution
For the strictly positive case (the suboptimal case) the maximum entropy
solution to the Leech problem and
, with and stable rational
matrix functions, is proved to be a stable rational matrix function. An
explicit state space realization for is given, and turns out
to be strictly less than one. The matrices involved in this realization are
computed from the matrices appearing in a state space realization of the data
functions and . A formula for the entropy of is also given.Comment: 19 page
State space formulas for stable rational matrix solutions of a Leech problem
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 is, and . The solution is given in the form of a state space
realization, where the matrices involved in this realization are computed from
state space realizations of the data functions and .Comment: 25 page
State space formulas for a suboptimal rational Leech problem II: Parametrization of all solutions
For the strictly positive case (the suboptimal case), given stable rational
matrix functions and , the set of all solutions to the
Leech problem associated with and , that is, and
, is presented as the range of a linear
fractional representation of which the coefficients are presented in state
space form. The matrices involved in the realizations are computed from state
space realizations of the data functions and . On the one hand the
results are based on the commutant lifting theorem and on the other hand on
stabilizing solutions of algebraic Riccati equations related to spectral
factorizations.Comment: 28 page
All solutions to the relaxed commutant lifting problem
A new description is given of all solutions to the relaxed commutant lifting
problem. The method of proof is also different from earlier ones, and uses only
an operator-valued version of a classical lemma on harmonic majorants.Comment: 15 page
Krein systems
In the present paper we extend results of M.G. Krein associated to the
spectral problem for Krein systems to systems with matrix valued accelerants
with a possible jump discontinuity at the origin. Explicit formulas for the
accelerant are given in terms of the matrizant of the system in question.
Recent developments in the theory of continuous analogs of the resultant
operator play an essential role
The twofold Ellis-Gohberg inverse problem in an abstract setting and applications
In this paper we consider a twofold Ellis-Gohberg type inverse problem in an
abstract *-algebraic setting. Under natural assumptions, necessary and
sufficient conditions for the existence of a solution are obtained, and it is
shown that in case a solution exists, it is unique. The main result relies
strongly on an inversion formula for a block operator matrix whose
off diagonal entries are Hankel operators while the diagonal entries are
identity operators. Various special cases are presented, including the cases of
matrix-valued -functions on the real line and matrix-valued Wiener
functions on the unit circle of the complex plane. For the latter case, it is
shown how the results obtained in an earlier publication by the authors can be
recovered.Comment: 52 page
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