Filtering for Stochastic Uncertain Systems with Probabilistic Distributed Delay

This paper deals with the filtering problem for a class of discrete-time uncertain stochastic nonlinear systems with both the probabilisticly occurring distributed delay and external stochastic disturbances. The distributed delay is assumed to occur in a random way governed by a Bernoulli stochastic variable and be time-varying. The aim of the addressed filtering problem is to design a linear filter such that, for the admissible stochastic distributed time-varying delay, stochastic disturbances, norm-bounded uncertainties as well as stochastic nonlinearities, the error dynamics of the filtering process is mean-square stable. By using the linear matrix inequality (LMI) method, several sufficient conditions are established that guarantee the mean-square stability of the filtering error, and then the filter parameters are characterized by the solution to a set of LMIs.