Robust Adaptive Sliding Mode Control of Markovian Jump Systems with Uncertain Mode-dependent Time-varying Delays and Partly Unknown Transition Probabilities

摘要

This paper deals with the problems of stochastic stability and sliding modecontrol for a class of continuous-time Markovian jump systems withmode-dependent time-varying delays and partly unknown transition probabilities.The design method is general enough to cover a wide spectrum of systems fromthose with completely known transition probability rates to those withcompletely unknown transition probability rates. Based on some mode-dependentLyapunov-Krasovski functionals and making use of the free-connection weightingmatrices, new delay-dependent conditions guaranteeing the existence of linearswitching surfaces and the stochastic stability of sliding mode dynamics arederived in terms of linear matrix inequalities (LMIs). Then, a sliding modecontroller is designed such that the resulted closed-loop system's trajectoriesconverge to predefined sliding surfaces in a finite time and remain there forall subsequent times. This paper also proposes an adaptive sliding modecontroller design method which applies to cases in which mode-dependenttime-varying delays are unknown. All the conditions obtained in this paper arein terms of LMI feasibility problems. Numerical examples are given toillustrate the effectiveness of the proposed methods.