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Fault detection filter design for discrete-time switched linear systems with mode-dependent average dwell-time. (English) Zbl 1330.93227
Summary: This paper is concerned with the problem of the fault detection (FD) filter design for discrete-time switched linear systems with mode-dependent average dwell-time. The switching law is mode-dependent and each subsystem has its own average dwell-time. The FD filters are designed such that the augmented switched systems are asymptotically stable, and the residual signal generated by the filters achieves a weighted $$l_{2}$$-gain for some disturbances and guarantees an $$H_{-}$$ performance for the fault. By the aid of multiple Lyapunov functions combined with projection lemma, sufficient conditions for the design of the FD filters are formulated by linear matrix inequalities, furthermore, the filters gains are characterized in terms of the solution of a convex optimization problem. Finally, an application to boost convertor is given to illustrate the effectiveness and the applicability of the proposed design method.

##### MSC:
 93E11 Filtering in stochastic control theory 93C55 Discrete-time control/observation systems 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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