On Designing of Sliding-Mode Control for Stochastic Jump Systems

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Shi, Peng, Xia, Yuanqing, Liu, G. P and Rees, D (2006) On Designing of Sliding-Mode Control for Stochastic Jump Systems. IEEE Transactions on Automatic Control, 51 (1). pp. 97-103. ISSN 0018-9286

Abstract

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.

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Item type	Article
URI	https://vuir.vu.edu.au/id/eprint/3085
DOI	10.1109/TAC.2005.861716
Official URL	http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arn...
Subjects	Historical > FOR Classification > 0906 Electrical and Electronic Engineering Historical > Faculty/School/Research Centre/Department > Institute for Logistics and Supply Chain Management (ILSCM) Historical > FOR Classification > 0199 Other Mathematical Sciences Information Systems
Keywords	ResPubID18987, Markov processes, closed loop systems, continuous time systems, control system synthesis, linear matrix inequalities, linear systems, motion control, stability, stochastic systems, variable structure systems
Citations in Scopus	642 - View on Scopus
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