Sliding mode control for Markovian jump repeated scalar nonlinear systems with packet dropouts: The uncertain occurrence probabilities case

Abstract

This paper studies the sliding-mode-based control problem for a class of delayed Markovian jump repeated scalar nonlinear systems (RSNSs) subject to packet dropouts (PDs) and randomly occurring uncertainties (ROUs). Here, the phenomenon of the Markovian PDs is modeled by utilizing a random variable obeying Markov process. By using the Bernoulli distributed random variables, the ROUs under uncertain occurrence probabilities (UOPs) are characterized from the mathematical perspective. In addition, the time-delay considered is bounded time-varying with known upper and lower bounds. The attention is on designing a sliding-mode-based control method for Markovian jump RSNSs in the simultaneous presence of Markovian PDs, ROUs and time-varying delays. Specifically, the robustly asymptotically mean-square stability is ensured for corresponding sliding mode dynamics by proposing new sufficient criterion. Moreover, the reachability in discrete setting is analyzed, i.e., the state trajectories of the system from any initial condition are globally driven onto a small region nearby the pre-designed sliding surface in mean square sense by synthesizing a robust sliding mode control (SMC) law. Finally, the effectiveness of developed control method is verified by some simulations.