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Probability Analysis of Terminal Sliding Mode Control of Second‐Order Markovian Jump Systems
Author(s) -
Zhu Jiaming,
Yu Xinghuo,
Zhang Tianping,
Cao Zhiqiang,
Yang Yuequan,
Fang Yu
Publication year - 2016
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1208
Subject(s) - control theory (sociology) , sliding mode control , piecewise , nonlinear system , mathematics , terminal (telecommunication) , conditional probability , bounded function , jump , markov process , terminal sliding mode , mode (computer interface) , monotonic function , stability (learning theory) , control (management) , computer science , mathematical analysis , physics , statistics , operating system , telecommunications , quantum mechanics , artificial intelligence , machine learning
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.