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Filtering on nonlinear time-delay stochastic systems. (English) Zbl 1010.93099
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.

MSC:
93E11Filtering in stochastic control
93C23Systems governed by functional-differential equations
93C10Nonlinear control systems
93E15Stochastic stability