## Delay-dependent non-synchronized robust $${\mathcal H}_\infty$$ state estimation for discrete-time piecewise linear delay systems.(English)Zbl 1191.93132

Summary: This paper investigates the problem of delay-dependent robust $${\mathcal H}_\infty$$ filtering design for a class of uncertain discrete-time piecewise linear state-delayed systems where state space instead of measurable output space partitions are assumed so that filter implementation may not be synchronized with plant state trajectory transitions. The state delay is assumed to be time-varying and of an interval-like type. The uncertainties are assumed to have a structured linear fractional form. The objective is to design a piecewise linear state estimator guaranteeing the asymptotic stability of the resulting filtering error system with robust $${\mathcal H}_\infty$$ performance $$\gamma$$. Based on a new delay-dependent piecewise Lyapunov-Krasovskii functional combined with Finsler’s Lemma, a novel delay-dependent robust $${\mathcal H}_\infty$$ performance analysis result is first presented and the filter synthesis is then developed. It is shown that the filter gains can be obtained by solving a set of linear matrix inequalities, 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:

 93E10 Estimation and detection in stochastic control theory 93C55 Discrete-time control/observation systems 93B36 $$H^\infty$$-control

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### References:

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