The sufficient conditions for stability of linear time-varying systems with state delays

This paper studies the stabilization of the infinite-dimensional linear time-varying system with state delays ẋ = A(t)x + A1(t)x(t -h) + B(t)u. The operator A(t) is assumed to be the generator of a strong evolution operator. In contrast to the previous results, the stabilizability conditions are obt...

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Bibliographic Details
Main Author: Kreangkri Ratchagit
Format: Journal
Published: 2018
Subjects:
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=78649764511&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/50972
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Institution: Chiang Mai University
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Summary:This paper studies the stabilization of the infinite-dimensional linear time-varying system with state delays ẋ = A(t)x + A1(t)x(t -h) + B(t)u. The operator A(t) is assumed to be the generator of a strong evolution operator. In contrast to the previous results, the stabilizability conditions are obtained via solving a Riccati differential equation and do not involve any stability property of the evolution operator. Our conditions are easy to construct and to verify. We provide a step-by-step procedure for finding feedback controllers. © 2010, Academic Publications Ltd.