Robust Stability of Discrete Systems with Uncertainties and Random Delay

A new type of discrete system with random delay and uncertainties is proposed. The problem of robustly globally exponentially stable in the mean square sense for the proposed system is investigated. By defining a Lyapunov-Krasovskii functional by utilizing some new finite sum equalities for the bounding of cross term, a delay-distribution-dependent criterion is obtained. Different from the existing ones, the proposed criterion depends on not only the size of the delay but also the probability distribution of it. The conditions are represented in the form of linear matrix inequalities (LMIs). Numerical examples suggest that the results are effective and are an improvement over previous ones.