Non-fragile [formula omitted] finite-time sliding mode control for stochastic Markovian jump systems with time delay

Abstract

This article mainly discusses the realization of H∞ finite-time control for a class of uncertain stochastic time-delay systems with unmeasured states through sliding mode control (SMC). The purpose of this paper is to design a suitable SMC controller to suppress the influence of factors such as model switching and time delay on the system performance, so that the system state can be stabilized within a limited time interval. First, the state of the system is reconstructed through the H∞ state observer, and the SMC law based on the state observer is designed so that the state trajectory reaches the specified sliding surface (s.s.s) in a given finite time. Next, by introducing the concept of time-partitioning strategy, the finite-time boundedness (FTBs) of the reaching phase and the sliding motion phase are realized respectively. Then, according to the linear matrix inequality(LMI), the asymptotic stochastic stability of the system and sufficient conditions for sliding mode dynamics with a given interference attenuation level are derived. Finally, the numerical example and single-link robot arm model (S-lram) show the effectiveness of the method.