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Robust exponential \(H_\infty\) filtering for discrete-time switched fuzzy systems with time-varying delay. (English) Zbl 1346.93382

Summary: This paper considers \(H_\infty\) filtering of discrete-time uncertain switched nonlinear systems with time-varying delay via Takagi-Sugeno fuzzy model which is used to approximate each nonlinear subsystem. Fuzzy piecewise Lyapunov-Krasovskii functionals and average dwell time approaches are utilized for the exponential stability analysis and \(H_\infty\) filter design. A new sufficient condition is obtained to guarantee the exponential stability with a prescribed \(H_\infty\) performance index for the filtering error system. Filter parameter matrices can be obtained by solving sets of linear matrix inequalities. An example of an uncertain single-link robot arm is given to demonstrate the effectiveness of the proposed method.

MSC:

93E11 Filtering in stochastic control theory
93B36 \(H^\infty\)-control
93C10 Nonlinear systems in control theory
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