Delay-Dependent Robust H ∞ Filter Design for Uncertain Linear Systems with Time-Varying Delay

A new delay-dependent robust H∞ filtering design for uncertain linear systems with time-varying delay is investigated. Two kinds of time-varying delays are considered. One is differentiable uniformly bounded with a bounded delay derivative; the other is continuous uniformly bounded. A full-order filter is designed which ensures the asymptotic stability of the filtering error system and a prescribed level of H∞ performance for all possible parameters which reside in a given polytope. By constructing a new Lyapunov functional which contains a triple integral term, new delay-dependent conditions for the existence of the H∞ filter are derived which are less conservative than the existing ones. The filter gain can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, two numerical examples are given to show the effectiveness and the advantages of the proposed method. This work was supported by the National Science Foundation of China under Grant 60528002, and the Beijing Education Committee Cooperation Building Foundation Project. J. Sun ( ) · J. Chen School of Automation, Beijing Institute of Technology, Beijing 100081, China e-mail: [email protected] J. Chen e-mail: [email protected] J. Sun · G.P. Liu · D. Rees Faculty of Advanced Technology, University of Glamorgan, Pontypridd CF37 1DL, UK G.P. Liu e-mail: [email protected] D. Rees e-mail: [email protected] G.P. Liu Key Laboratory of Complex Systems and Intelligent Science, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China 764 Circuits Syst Signal Process (2009) 28: 763–779