On Designing of Sliding-Mode Control for Stochastic Jump Systems

Guoping Liu, Peng Shi, David Rees, Yuanqing Xia

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)97 - 103
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number1
Publication statusPublished - 16 Jan 2006


  • linear matrix inequality (lmi)
  • markovian jump parameter
  • sliding-mode control
  • stochastic stability


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