H∞ sliding mode control for Markovian jump systems with randomly occurring uncertainties and repeated scalar nonlinearities via delay-fractioning method

This paper addresses the problem of robust H_∞ sliding mode control (SMC) for discrete delayed Markovian jumping systems subject to randomly occurring uncertainties (ROUs) and repeated scalar nonlinearities (RSNs). Here, a set of mutually independent Bernoulli distributed random variables is introduced to model the phenomenon of the ROUs, where the occurrence probabilities could be uncertain. The purpose of paper is to present an H_∞ SMC strategy via the delay-fractioning approach such that, for the Markovian jumping parameters, time-varying delays, ROUs and RSNs, the mean-square stability of the resulted sliding motion with a prescribed H_∞ performance can be guaranteed. Subsequently, the robust sliding mode controller is synthesized to guarantee that the reachability condition in the discrete-time setting is ensured. Finally, the validity of proposed robust SMC strategy is verified by providing a simulation example.