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Qiuqiu Fan,Zhao-Yan Li,Longsuo Li 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.2
This article aims to explore the stability and stabilization of a more practical class of stochastic neutraltype Markovian jump time-delay systems (SNMJTDSs) with two delays in the derivative. First, a less restrictive condition is imposed on the associated difference operator to ensure its stability. Second, by constructing novel Lyapunov-Krasovskii functionals, sufficient conditions for exponential stability (in the sense of mean square and almost sure) are established. Then, the SNMJTDS is stabilized by designing a delayed feedback controller. Finally, the less conservativeness of the proposed stability criterion and the validity of the designed controller are checked through two examples.
Lei Zhao,Qiuqiu Fan 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.2
In this paper, it is proved that an unstable highly nonlinear hybrid stochastic functional differential equation with infinite delay (HNHISFDE) can be stabilized by designing a controller that not only depends on discretetime state observations, but only produces different time lags in each observation. Firstly, common conditions are imposed on the original system to ensure the existence and uniqueness of the solution. Secondly, the design method of delay feedback control is presented to stabilize a class of HNHISFDEs. Notably, new assumptions based on Lyapunov functional and M-matrix methods are provided to construct the controller step by step. Then, the sufficient criteria of H∞ stabilization, asymptotic stabilization and exponential stabilization are established by applying the Lyapunov stability theory. Finally, the effectiveness of the theoretical results is illustrated by a numerical example.