Probability Analysis of Terminal Sliding Mode Control of Second-Order Markovian Jump Systems

This paper explores the probability problems on terminal sliding mode control of second‐order nonlinear continuous Markovian jump systems. An equivalent control based terminal sliding mode control scheme is proposed that can guarantee the systems' finite time mean‐square stability. By introduci...

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Published inAsian journal of control Vol. 18; no. 4; pp. 1385 - 1394
Main Authors Zhu, Jiaming, Yu, Xinghuo, Zhang, Tianping, Cao, Zhiqiang, Yang, Yuequan, Fang, Yu
Format Journal Article
LanguageEnglish
Published Hoboken Blackwell Publishing Ltd 01.07.2016
Wiley Subscription Services, Inc
Subjects
conditional probability
Markov analysis
Markovian jump system
mean-square stability
Nonlinear systems
Probability
Terminal sliding mode control
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Summary:This paper explores the probability problems on terminal sliding mode control of second‐order nonlinear continuous Markovian jump systems. An equivalent control based terminal sliding mode control scheme is proposed that can guarantee the systems' finite time mean‐square stability. By introducing a multi‐step transition conditional probability, the novel reaching and sliding probabilities are derived for the situations where the control force is not strong enough. This indicates that the reaching and sliding probabilities are both monotonically bounded non‐decreasing non‐negative piecewise right‐continuous functions of the control parameter. A numerical example is given to show the feasibility of the theoretical results.
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ISSN:1561-8625
1934-6093
DOI:10.1002/asjc.1208