\(\mathcal{H}_\infty\) filtering for a class of discrete-time switched fuzzy systems. (English) Zbl 1292.93133
Summary: This paper focuses on \(\mathcal{H}_\infty\) filtering problem for a class of discrete-time switched nonlinear system under both fast and slow switching property. Each nonlinear mode of the switched system is expressed by a set of linear systems in local regions via T-S fuzzy modeling. Based on mode-dependent and fuzzy-basis-dependent Lyapunov functions, existence conditions for the desired full-order filters are derived such that the developed filtering error system is globally uniformly asymptotically stable with a given \(\mathcal{H}_\infty\) performance index. In particular, the mode-dependent average dwell time switching scheme is proposed for slow switching to relax the restrictions of average dwell time. Finally, the validity and potential of the developed theoretical results are demonstrated by a numerical example.
MSC:
| 93E11 | Filtering in stochastic control theory |
| 93B36 | \(H^\infty\)-control |
| 93C42 | Fuzzy control/observation systems |
Keywords:
mode dependent average dwell time; \(\mathcal{H}_\infty\) filtering; switched systems; fuzzy systemsReferences:
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