The Kalman-Yakubovich-Popov Lemma for Pritchard-Salamon systems

DOI10.1016/0167-6911(95)00045-3zbMath0877.93065OpenAlexW1987414514WikidataQ124998288 ScholiaQ124998288MaRDI QIDQ672724

Ruth F. Curtain

Publication date: 28 February 1997

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-6911(95)00045-3

zbMATH Keywords

Riccati equationsRiccati inequalitiesLyapunov inequalitiesKalman-Yakubovich-Popov LemmaComparison theorem for Riccati equationsInfinite-dimensional systemsPositive realPritchard-Salamon classUnbounded inputs and outputs

Mathematics Subject Classification ID

Popov-type stability of feedback systems (93D10) Operator-theoretic methods (93B28) Control/observation systems in abstract spaces (93C25)

Related Items (6)

Kalman-Popov-Yakubovich Lemma and the \(S\)-procedure: a historical essay ⋮ Representations and regularity of vector-valued right-shift invariant operators between half-line Bessel potential spaces ⋮ Corrections to ``The Kalman-Yakubovich-Popov lemma for Pritchard-Salamon systems ⋮ Design of consensus and adaptive consensus filters for distributed parameter systems ⋮ The Kalman-Yakubovich-Popov theorem for stabilizable hyperbolic boundary control systems ⋮ Well-posedness and admissible stabilizability for Pritchard-Salamon systems

Cites Work

• Comparison theorems for infinite-dimensional Riccati equations
• A frequency theorem for the case in which the state and control spaces are Hilbert spaces, with an application to some problems in the synthesis of optimal controls. I
• A frequency theorem for the case in which the state and control spaces are Hilbert spaces, with an application to some problems of synthesis of optimal controls. II
• On a generalization of the Kalman-Yakubovic lemma
• LYAPUNOV FUNCTIONS FOR THE PROBLEM OF LUR'E IN AUTOMATIC CONTROL
• On Frequency Domain Stability for Evolution Equations in Hilbert Spaces via the Algebraic Riccati Equation
• Equivalent Conditions for the Solvability of the Nonstandard $LQ$-Problem for Pritchard–Salamon Systems
• A System Theory Criterion for Positive Real Matrices
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