Asynchronous nonfragile \(H_\infty\) filtering for discrete-time nonlinear switched systems with quantization. (English) Zbl 1478.93700
Summary: This paper investigates the nonfragile \(H_\infty\) filtering problem for a class of discrete-time nonlinear switched systems with quantization. The nonlinearity considered in our work is assumed to satisfy the Lipschitz conditions. The asynchronous switching is taken into consideration in the filter design. To study the asynchronous switching, a lag is introduced between the switching of subsystem and its matched filter. The Lyapunov functions are allowed to increase during the running time of activated subsystem with its mismatched filter. Both the measurement output signal and the performance output signal are quantized by two static quantizers before being transmitted, respectively. This consideration of quantization is more practical than the case that the signal quantization only exists in the measurement output signal. The main attention of this paper is to design a set of mode-dependent nonfragile \(H_\infty\) filters such that the filtering error systems are globally uniformly asymptotically stable and satisfy a weighted \(H_\infty\) performance index. Based on the average dwell time approach and multiple Lyapunov functions, sufficient conditions are established in the form of linear matrix inequalities (LMIs). The desired nonfragile \(H_\infty\) filters can be obtained by solving these LMIs. Finally, an example is provided to illustrate the effectiveness of the obtained results.
MSC:
| 93E11 | Filtering in stochastic control theory |
| 93B36 | \(H^\infty\)-control |
| 93C55 | Discrete-time control/observation systems |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C10 | Nonlinear systems in control theory |
Keywords:
nonlinear switched systems; \( H_\infty\) filtering; nonfragile; quantization; average dwell timeReferences:
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