Robust H∞ filtering for discrete-time systems with Markovian switching and time-delays

The robust Hfiltering problem for uncertain discrete-time Markovian jump linear systems with modedependent time-delays is investigated.Attention is focused on designing a Markovian jump linear filter that ensures robust stochastic stability while achieving a prescribed Hperformance level of the resulting filtering error system, for all admissible uncertainties.The key features of the approach include the introduction of a new type of stochastic Lyapunov functional and some free weighting matrix variables.Sufficient conditions for the solvability of this problem are obtained in terms of a set of linear matrix inequalities.Numerical examples are provided to demonstrate the reduced conservatism of the proposed approach.