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New results on robust ${H}_{\infty }$ filtering design for discrete-time piecewise linear delay systems. (English) Zbl 1154.93348
Summary: This paper revisits the problem of robust ${H}_{\infty }$ filtering design for a class of discrete-time piecewise linear state-delayed systems. The state delay is assumed to be time-varying and of an interval-like type, which means that both the lower and upper bounds of the time-varying delay are available. The parameter uncertainties are assumed to have a structured linear fractional form. Based on a novel delay-dependent piecewise Lyapunov-Krasovskii functional combined with Finsler’s Lemma, a new delay-dependent sufficient condition for robust ${H}_{\infty }$ performance analysis is first derived and then the filter synthesis is developed. It is shown that by using a new linearisation technique, a unified framework can be developed so that both the full-order and reduced-order filters can be obtained by solving a set of linear matrix inequalities (LMIs), which are numerically efficient with commercially available software. Finally, a numerical example is provided to illustrate the effectiveness and less conservatism of the proposed approach.
##### MSC:
 93B36 ${H}^{\infty }$-control 93C55 Discrete-time control systems