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On designing of sliding-mode control for stochastic jump systems

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4 Author(s)
Peng Shi ; Sch. of Technol., Univ. of Glamorgan, Pontypridd, UK ; Yuanqing Xia ; Liu, G.P. ; Rees, D.

In this note, we consider the problems of stochastic stability and sliding-mode control for a class of linear continuous-time systems with stochastic jumps, in which the jumping parameters are modeled as a continuous-time, discrete-state homogeneous Markov process with right continuous trajectories taking values in a finite set. By using Linear matrix inequalities (LMIs) approach, sufficient conditions are proposed to guarantee the stochastic stability of the underlying system. Then, a reaching motion controller is designed such that the resulting closed-loop system can be driven onto the desired sliding surface in a limited time. It has been shown that the sliding mode control problem for the Markovian jump systems is solvable if a set of coupled LMIs have solutions. A numerical example is given to show the potential of the proposed techniques.

Published in:

Automatic Control, IEEE Transactions on  (Volume:51 ,  Issue: 1 )