Robust H_∞ filtering for stochastic time-delay systems with missing measurements

In this paper, the robust H_∞ filtering problem is studied for stochastic uncertain discrete time-delay systems with missing measurements. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. We aim to design filters such that, for all possible missing observations and all admissible parameter uncertainties, the filtering error system is exponentially mean-square stable, and the prescribed H_∞ performance constraint is met. In terms of certain linear matrix inequalities (LMIs), sufficient conditions for the solvability of the addressed problem are obtained. When these LMIs are feasible, an explicit expression of a desired robust H_∞ filter is also given. An optimization problem is subsequently formulated by optimizing the H_∞ filtering performances. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach. © 2006 IEEE.