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Reliable $H_{\infty}$ control of multiple time scales singularly perturbed systems with sensor failure. (English) Zbl 1162.93335
Summary: This paper studies the reliable $H_{\infty}$ control for linear time-invariant multiparameter singularly perturbed systems against sensor failures. By time-scale decomposition, the full-order system is decomposed into slow and fast subsystems. After designing a reliable $H_{\infty}$ controller for the global system, three reduced reliable $H_{\infty}$ sub-controllers based on the slow and fast problems are obtained through the manipulation of the algebraic Riccati equations. The resulting control systems are reliable in that they provide guaranteed asymptotic stability and $H_{\infty}$ performance when all control components are operational as well as when sensor failures occur.

##### MSC:
 93B36 $H^\infty$-control 93C73 Perturbations in control systems 93C05 Linear control systems
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