Exponential H∞ filtering for uncertain discrete-time switched linear systems with average dwell time: A µ-dependent approach
Date
2008
Authors
Zhang, L.
Boukas, E.
Shi, P.
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Journal article
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International Journal of Robust and Nonlinear Control, 2008; 18(11):1188-1207
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Lixian Zhang, El-Kebir Boukas and Peng Shi
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Abstract
<jats:title>Abstract</jats:title><jats:p>In this paper, the problem of exponential<jats:italic>H</jats:italic><jats:sub>∞</jats:sub>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‐<jats:italic>dependent</jats:italic>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<jats:italic>H</jats:italic><jats:sub>∞</jats:sub>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. Copyright © 2007 John Wiley & Sons, Ltd.</jats:p>
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Copyright © 2007 John Wiley & Sons, Ltd.