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Robust \(H_{\infty }\)-filter design for neutral stochastic uncertain systems with time-varying delay. (English) Zbl 1161.93025
Summary: The robust \(H_{\infty }\) filtering problem for a class of neutral stochastic systems is discussed. The system under consideration contains parameter uncertainties, Itô-type stochastic disturbances, and time-varying delay. The parameter uncertainties are assumed to be time-varying norm-bounded. Using the stochastic Lyapunov stability theory and Itô’s differential rule, a full-order filter is designed for all admissible uncertainties and time-varying delay, which is expressed in the form of linear matrix inequality. The dynamics of the filtering error systems are guaranteed to be robust stochastically mean square asymptotically stable, while achieving a prescribed stochastic robust \(H_{\infty }\) performance level. At the end of this paper, a numerical example is given to demonstrate the usefulness of the proposed method.

MSC:
93E11 Filtering in stochastic control theory
34K40 Neutral functional-differential equations
15A39 Linear inequalities of matrices
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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