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Delay-dependent observer-based ${H}_{\infty }$ finite-time control for switched systems with time-varying delay. (English) Zbl 1244.93045
Summary: This paper is concerned with the problem of observer design for switched linear systems with time-varying delay and exogenous disturbances. The attention is focused on designing the full-order observers that guarantee the finite-time bounded and ${H}_{\infty }$ finite-time stability of the dynamic augmented system. Based on Linear Matrix Inequalities (LMIs) technology and an Average Dwell Time (ADT) approach, sufficient conditions which ensure the observer-based finite-time bounded and ${H}_{\infty }$ finite-time stability are given, respectively. By using a state observer, the memory state feedback controller is designed to finite-time stabilize a time-delay switched system, and the conditions are formulated in terms of delay-dependent LMIs. An example is given to illustrate the efficiency of the proposed methods.
##### MSC:
 93B36 ${H}^{\infty }$-control 93C30 Control systems governed by other functional relations 93B52 Feedback control 93B07 Observability
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