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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.

international journal of dynamics and control

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