Probability‐dependent gain‐scheduled control for discrete stochastic delayed systems with randomly occurring nonlinearities

In this paper, the gain‐scheduled control problem is addressed by using probability‐dependent Lyapunov functions for a class of discrete‐time stochastic delayed systems with randomly occurring sector nonlinearities. The sector nonlinearities are assumed to occur according to a time‐varying Bernoulli distribution with measurable probability in real time. The multiplicative noises are given by means of a scalar Gaussian white noise sequence with known variances. The aim of the addressed gain‐scheduled control problem is to design a controller with scheduled gains such that, for the admissible randomly occurring nonlinearities, time delays and external noise disturbances, the closed‐loop system is exponentially mean‐square stable. Note that the designed gain‐scheduled controller is based on the measured time‐varying probability and is therefore less conservative than the conventional controller with constant gains. It is shown that the time‐varying controller gains can be derived in terms of the measurable probability by solving a convex optimization problem via the semi‐definite programme method. A simulation example is exploited to illustrate the effectiveness of the proposed design procedures. Copyright © 2012 John Wiley & Sons, Ltd.