Zhang, Lixian, Boukas, El-Kébir and Shi, Peng (2008) Exponential H filtering for uncertain discrete-time switched linear systems with average dwell time: A μ-dependent approach. International Journal of Robust and Nonlinear Control, 18 (11). pp. 1188-1207. ISSN 1049-8923

Abstract

In this paper, the problem of exponential H∞ filter problem for a class of discrete-time polytopic uncertain switched linear systems with average dwell time switching is investigated. The exponential stability result of the general discrete-time switched systems using a discontinuous piecewise Lyapunov function approach is first explored. Then, a new µ-dependent approach is proposed, which means the analysis or synthesis of the underlying systems is dependent on the increase degree µ of the piecewise Lyapunov function at the switching instants. A mode-dependent full-order filter is designed such that the developed filter error system is robustly exponentially stable and achieves an exponential H∞ performance. Sufficient existence conditions for the desired filter are derived and formulated in terms of a set of linear matrix inequalities, and consequently the minimal average dwell time and the corresponding filter are obtained from such conditions for a given system decay degree. A numerical example is presented to demonstrate the potential and effectiveness of the developed theoretical results.

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