TY - JOUR

T1 - On Designing of Sliding-Mode Control for Stochastic Jump Systems

AU - Liu, Guoping

AU - Shi, Peng

AU - Rees, David

AU - Xia, Yuanqing

PY - 2006/1/16

Y1 - 2006/1/16

N2 - 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.

AB - 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.

KW - linear matrix inequality (lmi)

KW - markovian jump parameter

KW - sliding-mode control

KW - stochastic stability

U2 - 10.1109/TAC.2005.861716

DO - 10.1109/TAC.2005.861716

M3 - Article

SN - 0018-9286

VL - 51

SP - 97

EP - 103

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 1

ER -