Stability of highly non‐linear switched stochastic systems

Zhao, Ying; Wu, Xiaotai; Cao, Jinde

doi:10.1049/iet-cta.2019.0033

Cited by 5 publications

(10 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent years, highly nonlinear hybrid stochastic systems have been widely studied, and their coefficients do not satisfy the linear growth condition (LGC) 10‐18 . As is known to all, the LGC and the LLC are assumed simultaneously in the classical results to guarantee the existence and uniqueness of the solution of linear stochastic systems.…”

Section: Introductionmentioning

confidence: 99%

“…These progresses mainly focuses on highly nonlinear stochastic systems with Markovian switching signals. Moreover, stability of highly nonlinear SSSs were considered in Reference 17, where the subsystems were active according to deterministic switching signals.…”

Section: Introductionmentioning

confidence: 99%

“…It is worthy of pointing out that the generalized Itô formula is effective in considering the stability of stochastic systems with Markovian switching, 19‐21,23 which is hardly applied to deal with the stability of stochastic systems with deterministic switching signals. For stochastic systems with deterministic switching signals, the existence and stability should be investigated in each switching interval by using the average dwell time (ADT) method 17,26 . Recently, the existence and stability are presented for highly nonlinear SSSs without time delays 17 .…”

Section: Introductionmentioning

confidence: 99%

“…For stochastic systems with deterministic switching signals, the existence and stability should be investigated in each switching interval by using the average dwell time (ADT) method 17,26 . Recently, the existence and stability are presented for highly nonlinear SSSs without time delays 17 . The method in Reference 17 cannot be further extended to study highly nonlinear SSSs with time delays.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the existence and stability are presented for highly nonlinear SSSs without time delays 17 . The method in Reference 17 cannot be further extended to study highly nonlinear SSSs with time delays. And the stability of highly nonlinear hybrid SDDEs was studied by delay feedback control, 19 whose switching signals were Markovian switching signals.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Stabilization by delay feedback control for highly nonlinear switched stochastic systems with time delays

Zhao

Zhu

2021

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

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 pth 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.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%