Delay-Range-Dependent L 2–L ∞ Filtering for Stochastic Systems with Time-Varying Interval Delay

This paper focuses on the problem of delay-range-dependent L ₂–L _∞ filter design for stochastic systems with time-varying delay. The time delay varies in an interval. A delay-range-dependent sufficient condition is formulated in terms of linear matrix inequalities (LMIs), which guarantees the existence of a linear filter. The proposed filter ensures that the filtering error system is stochastically asymptotically stable and that its L ₂–L _∞ performance satisfies a prescribed level. The corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. This work is partially supported by the Natural Science Foundation of China (60674055, 60774047), and the Taishan Scholar Programme of Shandong Province.