Sliding mode control for networked systems with randomly varying nonlinearities and stochastic communication delays under uncertain occurrence probabilities

In this paper, we aim to propose the robust sliding mode control (SMC) scheme for discrete networked systems subject to randomly occurring uncertainty (ROU), randomly varying nonlinearities (RVNs) and multiple stochastic communication delays (MSCDs). Here, a series of mutually independent Bernoulli distributed random variables is introduced to model the phenomena of the ROU, RVNs and MSCDs, where the occurrence probabilities of above phenomena are allowed to be uncertain. For the addressed systems, an SMC strategy is given such that, for above network-induced phenomena, the stability of the resulted sliding motion can be guaranteed by presenting a new delay-dependent sufficient criterion via the delay-fractioning method. Moreover, the discrete sliding mode controller is synthesized such that the state trajectories of the system are driven onto a neighborhood of the specified sliding surface and remained thereafter, i.e., the reachability condition in discrete-time setting is verified. Finally, the usefulness of the proposed SMC method is illustrated by utilizing a numerical example.