Open AccessNew results on stability for non‐linear Markov switched stochastic functional differential systems
Author(s) -
Feng Lichao,
Liu Lei,
Cao Jinde,
Xue Changfeng
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2020.0833
Subject(s) - exponential stability , markov chain , mathematics , control theory (sociology) , stability (learning theory) , polynomial , markov process , linear system , lyapunov function , mathematical optimization , computer science , nonlinear system , mathematical analysis , statistics , physics , control (management) , quantum mechanics , artificial intelligence , machine learning
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.