Exponential $H_{\infty }$ Filter Design for Discrete Time-Delay Stochastic Systems With Markovian Jump Parameters and Missing Measurements

In this paper, the exponential H_∞ filtering problem is studied for discrete time-delay stochastic systems with Markovian jump parameters and missing measurements. The measurement missing phenomenon, which is related to the modes of subsystems, is described in the form of random matrix function and the missing probability of each sensor at every mode is governed by an individual random variable taking values in the interval [0,1] . This description of missing measurements is more general than the existing ones, where the missing probability is described by a Bernoulli distribution white sequence or a certain diagonal matrix. By using Lyapunov method and the properties of conditional mathematical expectation, we propose a novel approach to achieve the delay-dependent exponential stability criterion such that the filtering error system is mean-square exponentially stable and satisfies a prescribed H_∞ performance level. Moreover, there is no equation restriction on decay rate. Then, based on the obtained sufficient criterion, the filter matrices can be directly characterized by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the validity of the main result.