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Robust \(H_{\infty }\) filtering for a class of uncertain linear systems with time-varying delay. (English) Zbl 1138.93058

Summary: This paper deals with the problem of delay-dependent robust \(H_{\infty }\) filtering for uncertain linear systems with time-varying delay. Two cases of time-varying delays are fully considered; one is the time-varying delay being continuous uniformly bounded while the other is the time-varying delay being differentiable uniformly bounded with delay-derivative bounded by a constant. A stable linear filter is designed to ensure that the filtering error system is asymptotically stable with a prescribed level of \(H_{\infty }\) noise attenuation. Based on a new integral inequality, delay-dependent sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities. Through deriving these conditions, neither model transformation nor bounding technique for cross terms is employed. Moreover, the relationship between the sufficient conditions for the two cases of time-varying delay is disclosed. Finally, two examples are also given to illustrate the effectiveness of the proposed methodology.

MSC:

93E11 Filtering in stochastic control theory
93C41 Control/observation systems with incomplete information
93C05 Linear systems in control theory
93E15 Stochastic stability in control theory
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