Delay-dependent H∞H∞ filtering for stochastic systems with Markovian switching and mixed mode-dependent delays

This paper studies the problem of H∞H∞ filtering for a class of stochastic systems with Markovian switching and mixed mode-dependent time-varying delays. By introducing slack matrix variables and using Markovian switching Lyapunov functionals, we obtain delay-dependent sufficient conditions which guarantee the existence of H∞H∞ filters such that the filtering error system is exponentially mean-square stable and satisfies a prescribed H∞H∞ performance level; the conditions are in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H∞H∞ filter is given. Numerical examples are provided to demonstrate the effectiveness and the reduced conservatism of our results.