Stabilization of linear continuous time-varying systems with state delays in Hilbert spaces (Q2753141)
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scientific article; zbMATH DE number 1667108
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stabilization of linear continuous time-varying systems with state delays in Hilbert spaces |
scientific article; zbMATH DE number 1667108 |
Statements
24 January 2002
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stabilization
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time-varying
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delay system
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Riccati equation
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infinite-dimensional linear system
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strong evolution operator
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stabilizability
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nonlinear perturbations
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Stabilization of linear continuous time-varying systems with state delays in Hilbert spaces (English)
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The author considers the stabilization of the infinite-dimensional linear time varying system with state delays NEWLINE\[NEWLINE\dot x= A(t)x+ A_1(t) x(t- h)+ B(t) u,NEWLINE\]NEWLINE where the operator \(A(t)\) is assumed to be the generator of a strong evolution operator.NEWLINENEWLINENEWLINEIn contrast to previous results, the stabilizability conditions are obtained via solving a Riccati differential equation and do not involve any stability property of the evolution operator.NEWLINENEWLINENEWLINEThey provide a step-by-step procedure for finding feedback controllers and state stability conditions for some linear delay control systems with nonlinear perturbations.
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