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Zbl 1010.93099
Wang, Zidong; Ho, Daniel W.C.
Filtering on nonlinear time-delay stochastic systems. (English)
[J] Automatica 39, No.1, 101-109 (2003). ISSN 0005-1098

This paper considers the filtering problem for a general class of nonlinear time-delay stochastic systems. The main goal is to design a full-order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially ultimately bounded in the mean square. Both filter analysis and synthesis problems are considered. Sufficient conditions are proposed for the existence of desired exponential filters, which are expressed in terms of the solutions to algebraic Riccati inequalities involving scalar parameters. The explicit characterization of the desired filters is also derived. The method relies not on optimization theory but on Lyapunov-type stochastic stability results. A simulation example is given to illustrate the design procedures and performances of the proposed method.
[Vjatscheslav Vasiliev (Tomsk)]

MSC 2000:: *93E11 Filtering in stochastic control
93C23 Systems governed by functional-differential equations
93C10 Nonlinear control systems
93E15 Stochastic stability

Keywords: nonlinear filtering; stochastic exponential ultimate boundedness; time-delay systems; algebraic Riccati inequalities; exponential filters; stochastic stability

Cited in: Zbl 1215.93142

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