Stochastic Stability and H∞ Disturbance Attenuation of A Class of Nonlinear Stochastic Delayed Systems

In this paper, we consider stochastic stability analysis and H∞ disturbance attenuation for a class of discrete-time nonlinear stochastic retarded systems whose nonlinearities are described by statistical means. First a sufficient condition on mean square stability, which is independent of delay, is proposed using the stochastic Lyapunov functional approach. Then, H∞ disturbance attenuation property of the system is analyzed. It is shown that the H∞ disturbance attenuation of such nonlinear systems can be reduced to a linear matrix inequality problem.