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Wu, Huai-Ning; Wang, Jun-Wei; Shi, Peng

A delay decomposition approach to \({\mathcal L}_2-{\mathcal L}_\infty\) filter design for stochastic systems with time-varying delay. (English) Zbl 1220.93077

Automatica 47, No. 7, 1482-1488 (2011).
Summary: This paper investigates the problem of \({\mathcal L}_2-{\mathcal L}_\infty\) filter design for a class of stochastic systems with time-varying delay. The addressed problem is the design of a full order linear filter such that the error system is asymptotically mean-square stable and a prescribed \({\mathcal L}_2-{\mathcal L}_\infty\) performance is satisfied. In order to develop a less conservative filter design, a new Lyapunov-Krasovskii functional (LKF) is constructed by decomposing the delay interval into multiple equidistant subintervals, and a new integral inequality is established in the stochastic setting. Then, based on the LKF and integral inequality, the delay-dependent conditions for the existence of \({\mathcal L}_2-{\mathcal L}_\infty\) filters are obtained in terms of Linear Matrix Inequalities (LMIs). The resulting filters can ensure that the error system is asymptotically mean-square stable and the peak value of the estimation error is bounded by a prescribed level for all possible bounded energy disturbances. Finally, two examples are given to illustrate the effectiveness of the proposed method.

Cited in 18 Documents

MSC:

93E11 Filtering in stochastic control theory
93E15 Stochastic stability in control theory

Keywords:

filter design; \({\mathcal L}_2-{\mathcal L}_\infty\) performance; linear matrix inequality (LMI); stochastic systems; time delay

Software:

LMI toolbox
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Full Text: DOI

References:

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