Asymptotic stability of neutral stochastic pantograph systems with Markovian switching

ABSTRACT

This paper investigates the asymptotic stability of neutral stochastic pantograph systems with Markovian switching (NSPSMS). The stochastic LaSalle theorem has been set up to locate the attractive sets for NSPSMS without linear growth condition. Subsequently, combining the stochastic LaSalle theorem and uniformly continuous theory, almost surely asymptotic stability and pth moment asymptotic stability are analysed. Furthermore, we also present one new criterion on the pth moment polynomial stability and almost surely polynomial stability for NSPSMS, where the coefficients of the delay term are time invariable. Finally, three examples are provided to exhibit the efficiency of the proposed results.

KEYWORDS:

• neutral stochastic pantograph systems
• Markovian switching
• asymptotic stability
• polynomial stability

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research is jointly supported by the National Natural Science Foundation of China [62076039,61803046] and the Natural Science Foundation of Hubei Province [2021CFB543].