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Mixed \(\mathcal H_2\)/\(\mathcal H_\infty\) filtering for continuous-time polytopic systems: A parameter-dependent approach. (English) Zbl 1102.94033

Summary: The problem of mixed \(\mathcal H_2/\mathcal H_\infty\) filtering is investigated for continuous-time polytopic systems. Given a stable system whose parameters reside in a polytope and can be measured online, attention is focused on the design of parameter-dependent filters such that the filtering error system is asymptotically stable and has guaranteed \(\mathcal H_2\) and \(\mathcal H\infty\) performances with respect to different input signals. By introducing multiple Lyapunov functions, the parameter-dependent approach developed in this paper is able to yield much less conservative filters than the existing results. A numerical example is provided to show the effectiveness and reduced conservatism of the proposed theory.

MSC:

94C05 Analytic circuit theory
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
93E11 Filtering in stochastic control theory
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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