Exponential H∞ filtering for time-varying delay systems: Markovian approach

This paper discusses the H∞H∞ filtering problem for a class of deterministic systems with time-varying delays, where the stochastic property of time-varying delays described by Markovian approach is taken into consideration in filter design. Firstly, the delay interval is separated into several subintervals, which can be described by Markov process. Then, a new H∞H∞ filtering method for deterministic system with time-varying delay is given, whose filter can switch with time delay in terms of Markov process. Sufficient conditions for the existence of H∞H∞ filter are obtained as linear matrix inequalities, where the mode transition rates are known exactly or inexactly. Finally, numerical examples are used to demonstrate the utility of the given methods.