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Stochastic Stability and Stabilization of Singular It Ô ‐type Markovian Jump Systems with Uncertain Transition Rates: An LMI Approach
Author(s) -
Jiang Baoping,
Gao Cunchen,
Kao Yonggui
Publication year - 2018
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.1621
Subject(s) - control theory (sociology) , mathematics , linear matrix inequality , uniqueness , controller (irrigation) , stability (learning theory) , markov process , type (biology) , mathematical optimization , computer science , control (management) , mathematical analysis , statistics , artificial intelligence , machine learning , ecology , agronomy , biology
This paper investigates the stochastic stability and stabilization for a class of singular stochastic systems of Itô‐type with Markovian switching, the transition rates (TRs) in the jumping processes are uncertain. The aims are to establish sufficient conditions to ensure the considered system to be stochastically stable in the mean square sense, which is supported by a detailed proof of existence and uniqueness of the system solution, and to propose a controller such that the system can be stabilizable. The controller is first proposed and has advantage over traditional ones, the controller gain matrices are obtained by solving a strict linear matrix inequality (LMI). Finally, a numerical example is provided to illustrate the validity of the obtained methodology.