Minimal and optimal linear discrete time-invariant dissipative scattering systems

DOI10.1007/BF01191426zbMath0898.47005OpenAlexW2021238573MaRDI QIDQ1378057

D. R. Pik, Damir Z. Arov, Marinus A. Kaashoek

Publication date: 5 February 1998

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01191426

zbMATH Keywords

Hankel operatorstate spaceSchur classde Branges-Rovnyak normKalman-Yakubovich-Popov operator inequalityminimal and optimal realizationstar-optimal realizations of a rational matrix function

Mathematics Subject Classification ID

Linear operator inequalities (47A63) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Linear operator methods in interpolation, moment and extension problems (47A57) General systems theory (93A99) Scattering theory of linear operators (47A40) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48)

Related Items (9)

Bounded real lemma for structured noncommutative multidimensional linear systems and robust control ⋮ Schur parameters, Toeplitz matrices, and Kreĭn shorted operators ⋮ Generalized Schur-Nevanlinna functions and their realizations ⋮ Minimal passive realizations of generalized Schur functions in Pontryagin spaces ⋮ Conservative dilations of dissipative multidimensional systems: the commutative and non-commutative settings ⋮ Passive discrete-time systems with a Pontryagin state space ⋮ Optimal time-variant systems and factorization of operators. I: Minimal and optimal systems ⋮ On the theory of passive resistance systems with losses of scattering channels ⋮ Realizations for Schur upper triangular operators centered at an arbitrary point

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