\(H_\infty\) filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities. (English) Zbl 1283.93284

Wang, Zidong; Liu, Yurong; Liu, Xiaohui

Automatica 44, No. 5, 1268-1277 (2008).

Summary: In this paper, we deal with the robust \(H_\infty\) filtering problem for a class of uncertain nonlinear time-delay stochastic systems. The system under consideration contains parameter uncertainties, Itô-type stochastic disturbances, time-varying delays, as well as sector-bounded nonlinearities. We aim at designing a full-order filter such that, for all admissible uncertainties, nonlinearities and time delays, the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square, while achieving the prescribed \(H_\infty\) disturbance rejection attenuation level. By using the Lyapunov stability theory and Itô’s differential rule, sufficient conditions are first established to ensure the existence of the desired filters, which are expressed in the form of a linear matrix inequality (LMI). Then, the explicit expression of the desired filter gains is also characterized. Finally, a numerical example is exploited to show the usefulness of the results derived.

MSC:

93E11	Filtering in stochastic control theory
93C10	Nonlinear systems in control theory
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
93D30	Lyapunov and storage functions

Keywords:

Itô stochastic system; \(H_\infty\) filtering; robust filtering; nonlinear filtering; time delays; Lyapunov-Krasovskii functional; linear matrix inequality

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