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Strictly dissipative stabilization of multiple‐memory Markov jump systems with general transition rates: A novel event‐triggered control strategy
Author(s) -
Xie Wenqian,
Zhang Ruimei,
Zeng Deqiang,
Shi Kaibo,
Zhong Shouming
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.4856
Subject(s) - dissipative system , control theory (sociology) , jump , controller (irrigation) , markov chain , computer science , stability (learning theory) , transmission (telecommunications) , event (particle physics) , mathematics , transition rate matrix , control (management) , telecommunications , statistics , physics , quantum mechanics , artificial intelligence , machine learning , agronomy , biology
Summary This paper investigates the strictly dissipative stabilization problem for multiple‐memory Markov jump systems with network communication protocol. Firstly, for reducing data transmission, we put forward a novel mode‐dependent event‐triggered communication scheme based on aperiodically sampled data. Secondly, a Markov jump system with general transition rates is considered to make the result more applicable, where the transition rates of some jumping modes allow to be completely known, or partially known, or even completely unknown. Thirdly, a less restrictive Lyapunov‐Krasovskii functional, which is only required to be positive definite at end points of each subinterval of the holding intervals, is first introduced for event‐triggered control issue. Based on the above methods, a sufficient condition with less conservatism is obtained to ensure the stochastic stability and dissipativity of the resulting closed‐loop system. Meanwhile, an explicit design method of the desired controller is achieved. Finally, two numerical examples are presented to demonstrate the effectiveness and advantage of the proposed method.