Gao, Huijun; Lam, James; Wang, Changhong Mixed \(\mathcal H_2\)/\(\mathcal H_\infty\) filtering for continuous-time polytopic systems: A parameter-dependent approach. (English) Zbl 1102.94033 Circuits Syst. Signal Process. 24, No. 6, 689-702 (2005). 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. Cited in 9 Documents 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 Keywords:linear matrix inequality; mixed \(\mathcal H_2\)/\(\mathcal H_\infty\) filtering; parameter-dependent filter; polytopic systems PDFBibTeX XMLCite \textit{H. Gao} et al., Circuits Syst. Signal Process. 24, No. 6, 689--702 (2005; Zbl 1102.94033) Full Text: DOI