Delay-distribution-dependent robust H∞ control for discrete-time systems with stochastic delays

The problem of robust H-infinity control design for a class of discrete-time linear systems with stochastic delays and parameter uncertainties is studied. Firstly, a new modeling method is presented. By utilizing a stochastic variable which satisfies Bernoulli random binary distribution, the probability distributions of time delays are translated into parameter matrices of the transferred model. Based on the established model, an appropriate Lyapunov-Krasovskii functional is developed to investigate the problem of robust mean-square stability and H-infinity control design. The effectiveness and applicability of the proposed method are demonstrated by two numerical examples.