Sliding Mode Control with Randomly Occurring Uncertainties and Mixed Time Delays

Abstract

In this chapter, the robust SMC problem is studied for discrete-time uncertain nonlinear stochastic systems with mixed time delays. Both the sectorlike nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties (ROUs) and RONs obey certain mutually uncorrelated Bernoulli distributed white noise sequences with known conditional probabilities. The mixed time delays consist of both the discrete and the distributed delays. Sufficient conditions are established to ensure the stability of the system dynamics in the specified sliding surface by solving certain semidefinite programming problem. Moreover, a discrete-time SMC law is proposed to make sure that the reaching condition holds. Secondly, the proposed control method is extended to address a class of uncertain discrete-time Markovian jump systems with mixed delays.