New results on ℒ2 −ℒ℞ filter design for delayed stochastic systems by delay decomposition approach

This paper investigates the new results on ℒ2−ℒ℞ filter design for delayed stochastic systems by delay decomposition approach. Based on the Lyapunov functional method, sufficient condition are obtained to ensure the error systems are mean-square asymptotically stable. Then the ℒ2−ℒ℞ filters are designed in terms of linear matrix inequalities (LMIs). In order to develop less conservative results, a new integral inequality is established in the stochastic setting. Because we have carefully considered the ranges for the time-varying delays, our criteria can be applicable to both fast and slow time-varying delays. Meanwhile, by dividing the time-varying delays into multiple nonuniformly subintervals and choosing an appropriate Lyapunov functional, new delay-dependent stability criteria are obtained and formulated in terms of LMIs which can be easily checked in practice. Finally, a example is given to illustrate the effectiveness and advantages of the proposed results.