Two canonical passive state/signal shift realizations of passive discrete time behaviors

DOI10.1016/j.jfa.2009.05.029zbMath1190.47014OpenAlexW2161743903MaRDI QIDQ732048

Olof J. Staffans, Damir Z. Arov

Publication date: 9 October 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2009.05.029

zbMATH Keywords

Krein spacebehaviourpassiveconservativestate/signalquotient spaceinput mapoutput mappast/future mapDe Branges-Rovnyak model

Mathematics Subject Classification ID

Operator-theoretic methods (93B28) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Applications of operator theory in systems, signals, circuits, and control theory (47N70) Realizations from input-output data (93B15) Canonical models for contractions and nonselfadjoint linear operators (47A45) Linear operators on spaces with an indefinite metric (47B50) Operator colligations (= nodes), vessels, linear systems, characteristic functions, realizations, etc. (47A48) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (9)

Applications of de Branges Spaces of Vector-Valued Functions ⋮ Canonical Transfer-function Realization for Schur-Agler-class Functions of the Polydisk ⋮ Canonical conservative state/signal shift realizations of passive discrete time behaviors ⋮ Symmetries in special classes of passive state/signal systems ⋮ Canonical state/signal shift realizations of passive continuous time behaviors ⋮ Well-posed state/signal systems in continuous time ⋮ A conservative de Branges-Rovnyak functional model for operator Schur functions on \(\mathbb C^+\) ⋮ On passive and conservative state/signal systems in continuous time ⋮ De Branges-Rovnyak realizations of operator-valued Schur functions on the complex right half-plane

Cites Work

• A Kreĭn space coordinate free version of the de Branges complementary space
• Schur functions, operator colligations, and reproducing kernel Pontryagin spaces
• State/signal linear time-invariant systems theory. IV: Affine and generalized transfer functions of discrete time systems
• State/signal linear time‐invariant systems theory: passive discrete time systems
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