Transfer functions of infinite-dimensional systems: positive realness and stabilization

DOI10.1007/s00498-017-0203-zzbMath1386.93233OpenAlexW2764197971MaRDI QIDQ679683

Mark R. Opmeer, Chris Guiver, Hartmut Logemann

Publication date: 19 January 2018

Published in: MCSS. Mathematics of Control, Signals, and Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00498-017-0203-z

zbMATH Keywords

transfer functioninfinite-dimensional systempositive-real functionstabilization by feedbacksystem node

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Stabilization of systems by feedback (93D15) Input-output approaches in control theory (93D25) Linear systems in control theory (93C05) Operator-theoretic methods (93B28) 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)

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A rolled-off passivity theorem, Some spectral properties of operator-valued positive-real functions, The circle criterion for a class of sector-bounded dynamic nonlinearities, Representations and regularity of vector-valued right-shift invariant operators between half-line Bessel potential spaces, Low‐gain integral control for a class of discrete‐time Lur'e systems with applications to sampled‐data control, Infinite-Dimensional Lur'e Systems: Input-To-State Stability and Convergence Properties, Infinite-dimensional Lur'e systems with almost periodic forcing, Incremental input-to-state stability for Lur'e systems and asymptotic behaviour in the presence of Stepanov almost periodic forcing, A circle criterion for strong integral input-to-state stability, Stability and convergence properties of forced infinite-dimensional discrete-time Lur'e systems, Stability and Robust Regulation of Passive Linear Systems, The generalised singular perturbation approximation for bounded real and positive real control systems

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