New delay-dependent L2–L∞L2–L∞ filter design for stochastic time-delay systems

This paper investigates delay-dependent L2–L∞L2–L∞ performance analysis and filtering of stochastic systems with delays. Based on an auxiliary vector, an integral inequality in the stochastic setting is introduced. The proposed stochastic integral inequality reduces to some existing ones in the deterministic context, if there are no stochastic perturbations. By using this new integral inequality and free-weighting matrix technique, a simpler L2–L∞L2–L∞ performance analysis result with fewer dimensions of linear matrix inequality (LMI) and fewer variables is presented. The mathematical equivalence of the presented result and some existing one is established. A stochastic L2–L∞L2–L∞ filter which guarantees asymptotic mean-square stability of the filtering error system is designed in terms of LMIs. Both model transformations and and estimation for cross terms are avoided. Two illustrative examples are given to show the effectiveness of the method.