A delay decomposition approach to L 2 – L ∞ filter design for stochastic systems with time-varying delay

A delay decomposition approach to L 2 – L ∞ filter design for stochastic systems with... This paper investigates the problem of L 2 – L ∞ 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 L 2 – L ∞ 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 L 2 – L ∞ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Automatica Elsevier

A delay decomposition approach to L 2 – L ∞ filter design for stochastic systems with time-varying delay

Automatica, Volume 47 (7) – Jul 1, 2011

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Publisher
Elsevier
Copyright
Copyright © 2011 Elsevier Ltd
ISSN
0005-1098
DOI
10.1016/j.automatica.2011.02.021
Publisher site
See Article on Publisher Site

Abstract

This paper investigates the problem of L 2 – L ∞ 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 L 2 – L ∞ 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 L 2 – L ∞ 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.

Journal

AutomaticaElsevier

Published: Jul 1, 2011

References

  • Absolute stability of time-delay systems with sector bounded nonlinearity
    Han, Q.L.
  • A discrete delay decomposition approach to stability of linear retarded and neutral systems
    Han, Q.L.
  • Robust filtering with guaranteed energy-to-peak performance-an LMI approach
    Palhares, R.M.; Peres, P.L.D.
  • A delay decomposition approach to delay-dependent stability for linear systems with time-varying delays
    Zhang, X.M.; Han, Q.L.
  • Stability and stabilization of delayed T–S fuzzy systems: a delay partitioning approach
    Zhao, Y.; Gao, H.; Lames, J.; Du, B.

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