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Stability and Stabilization of Stochastic Neutral-type Markovian Jump Time-delay Systems with Two Delays

Qiuqiu Fan, Zhao-Yan Li*, and Longsuo Li
International Journal of Control, Automation, and Systems, vol. 20, no. 2, pp.365-374, 2022

Abstract : 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.

Keyword : Delayed state feedback, exponential stability, Markovian jump systems, neutral-type delay systems.

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