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Delay-dependent robust \({\mathcal H}_\infty\) of uncertain linear state-delayed systems. (English) Zbl 1041.93515

Summary: This paper examines the problems of robust stabilization and robust \(H_\infty\)-control for linear systems with a constant time delay in the state and subject to parameter uncertainty. Systems with norm-bounded parameter uncertainty will be considered and attention is focused on the design of linear memoryless state feedback controllers. We develop methods of robust stabilization and robust \(H_\infty\)-control which are dependent on the size of the delay and are based on the solution of linear matrix inequalities. The proposed methods can be easily extended to uncertain linear polytopic systems as well as to the case of multiple time delays.

MSC:

93B36 \(H^\infty\)-control
93C23 Control/observation systems governed by functional-differential equations
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