Robust mixed H 2 /H ∞ filtering for uncertain stochastic systems with interval time-varying delays

In this paper, we study the robust mixed H 2 /H ∞ filtering problem for uncertain Ito-type linear stochastic systems with interval time-varying delays in state equation, measurement and output. Based on a linear stochastic bounded real lemma and Lyapunov-Krasovskii approach, improved delay-dependent sufficient conditions, which guarantee globally asymptotical stability in probability and achieve prescribed performances, are proposed in terms of linear matrix inequalities (LMIs). The H ∞ filter can be obtained by solving a LMI. When the worst-case disturbance is considered in the design procedure, the H2 and mixed H 2 /H ∞ filtering problems are formulated as convex optimization problems with LMIs constraints and solved by minimizing the total estimation error energy. A simulation example is provided to illustrate the effectiveness of the proposed method and to confirm the desired robust filtering performance.