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Stabilization by delay feedback control for highly nonlinear switched stochastic systems with time delays
Author(s) -
Zhao Ying,
Zhu Quanxin
Publication year - 2021
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.5434
Subject(s) - dwell time , control theory (sociology) , nonlinear system , lipschitz continuity , mathematics , exponential stability , moment (physics) , stability (learning theory) , lyapunov function , function (biology) , control (management) , computer science , mathematical analysis , medicine , clinical psychology , physics , classical mechanics , quantum mechanics , artificial intelligence , machine learning , evolutionary biology , biology
This paper firstly discusses the existence and boundedness of unique global solution for highly nonlinear switched stochastic systems (SSSs) with time delays, where the switching signal is deterministic switching signal. Although the existence and boundedness of unique global solution can be obtained under local Lipschitz condition and Khasminskii‐type condition, highly nonlinear SSSs with time delays may not be stable. Therefore, a delay feedback control function can be designed for studying the stability of highly nonlinear SSSs with time delays, whose coefficients do not satisfy the linear growth condition. By using the Mathematical induction, Lyapunov function approach and the average dwell time method, H ∞ stability and the p th moment exponential stability are studied for highly nonlinear SSSs with time delays. An explanatory example is given to illustrate the effectiveness of the main results.