New results on stability for non-linear Markov switched stochastic functional differential systems
- Author(s): Lichao Feng 1, 2 ; Lei Liu 3 ; Jinde Cao 2, 4 ; Changfeng Xue 5
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View affiliations
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Affiliations:
1:
College of Science, and Hebei Key Laboratory of Data Science and Application , North China University of Science and Technology , Tangshan 063210 , People's Republic of China ;
2: The Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, and School of Mathematics , Southeast University , Nanjing 210096 , People's Republic of China ;
3: College of Science , Hohai University , Nanjing 210098 , People's Republic of China ;
4: Yonsei Frontier Lab , Yonsei University , Seoul 03722 , South Korea ;
5: School of Mathematics and Physics , Yancheng Institute of Technology , Yancheng 224051 , People's Republic of China
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Affiliations:
1:
College of Science, and Hebei Key Laboratory of Data Science and Application , North China University of Science and Technology , Tangshan 063210 , People's Republic of China ;
- Source:
Volume 14, Issue 20,
27
December
2020,
p.
3406 – 3416
DOI: 10.1049/iet-cta.2020.0833 , Print ISSN 1751-8644, Online ISSN 1751-8652
For Markov switched stochastic functional differential systems (SFDSs), asymptotic property is one of the most desired issues. Recently, a new class of delay-dependent asymptotic stability for non-linear Markov switched SFDSs was investigated. However, the existing references do not take the convergent speed and non-autonomous factor into consideration. Therefore, by means of multiple Lyapunov–Krasovskii functionals, this study is devoted to examine the exponential stability for highly non-linear autonomous Markov switched SFDSs and the exponential stability, polynomial stability and polynomial growth at most for highly non-linear non-autonomous systems, where all the criteria rely on the intervals lengths of continuous delays. In addition, the properties of boundedness and asymptotic stability are as well explored.
Inspec keywords: Lyapunov methods; differential equations; polynomials; delays; asymptotic stability; matrix algebra; stochastic systems
Other keywords: multiple Lyapunov–Krasovskii functionals; polynomial stability; asymptotic property; delay-dependent asymptotic stability; stochastic functional differential systems; nonlinear nonautonomous systems; nonlinear autonomous Markov; nonautonomous factor; SFDSs; nonlinear Markov; exponential stability
Subjects: Distributed parameter control systems; Mathematical analysis; Algebra; Time-varying control systems; Stability in control theory
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