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Stochastic Sliding Mode Control for Systems with Markovian Jump Parameters

Authors:Xia Yuanqing, University of Glamorgan, China
Shi Peng, University of Glamorgan, United Kingdom
Liu G. P., University of Glamorgan, United Kingdom
Rees D., University of Glamorgan, United Kingdom
Topic:1.4 Stochastic Systems
Session:Control of Jump Stochastic Processes
Keywords: Linear matrix inequality, markovian jump parameter, sliding modecontrol, stochastic stability


In this paper, the problems of stochastic stabilityand sliding mode control for a class of linear systems with stochastic jumps is considered, in which the jumping parameters aremodelled as a continuous-time, discrete-state homogeneous Markovprocess with right continuous trajectories taking values in afinite set. By using Linear matrix inequalities (LMI) approach,sufficient conditions are proposed to guarantee the stochasticstability of the underlying system. Then, a reaching motioncontroller is designed such that the resulting closed-loop systemcan be driven onto the desired sliding surface in a limited time.It has been shown that the sliding mode control problem for themarkovian jump systems is solvable if a set of coupled linearmatrix inequalities (LMIs) have solutions. A numerical example isgiven to show the potential of the proposed techni