State space theory of linear time invariant systems with delays in state, control, and observation variables. I, II

DOI10.1016/0022-247X(87)90098-9zbMath0643.93034MaRDI QIDQ1102240

J. Karrakchou, Michel C. Delfour

Publication date: 1987

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

observation operatorstime-invariantlinear time-invariant hereditary systemsstate space theorystructural operator

Mathematics Subject Classification ID

Linear systems in control theory (93C05) Operator-theoretic methods (93B28) Control problems for functional-differential equations (34K35) Control/observation systems in abstract spaces (93C25) Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) (93C30)

Related Items (9)

The regular linear systems associated with the shift semigroups and application to control linear systems with delay ⋮ Hamilton–Jacobi theory for hereditary control problems ⋮ Controllability properties of perturbed distributed parameter systems ⋮ Growth bound of delay-differential algebraic equations ⋮ The spectrum of unbounded operator matrices with non-diagonal domain ⋮ Factorization and quadratic cost problems in Hilbert spaces ⋮ Existence of solutions for a class of abstract neutral differential equations ⋮ Structure theory and duality for the time varying retarded functional differential equations ⋮ Quadratic optimal control through spectral and coprime factorisation

Cites Work

• F-controllability and observability of linear retarded systems
• The structural operator F and its role in the theory of retarded systems
• The structural operator F and its role in the theory of retarded systems. II
• Linear autonomous neutral functional differential equations
• Completeness and F-completeness of eigenfunctions associated with retarded functional differential equations
• Linear Functional Differential Equations as Semigroups on Product Spaces
• The Linear-Quadratic Optimal Control Problem with Delays in State and Control Variables: A State Space Approach
• The Largest Class of Hereditary Systems Defining a C₀ Semigroup on the Product Space
• The Infinite Time Quadratic Control Problem for Linear Systems with State and Control Delays: An Evolution Equation Approach
• Necessary and Sufficient Conditions of Approximate Controllability for General Linear Retarded Systems
• Quadratic Control of Evolution Equations with Delays in Control
• Equivalent Norms for Sobolev Spaces
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