Exponential stability of impulsive neutral stochastic functional differential equations with Markovian switching. (English) Zbl 07903283
Summary: The aim of this paper is to the discussion of the exponential stability of a class of impulsive neutral stochastic functional differential equations with Markovian switching. Under the influence of impulsive disturbance, the solution for the system is discontinuous. By using the Razumikhin technique and stochastic analysis approaches, as well as combining the idea of mathematical induction and classification discussion, some sufficient conditions for the \(p\)th moment exponential stability and almost exponential stability of the systems are obtained. The stability conclusion is full time-delay. The results show that impulse, the point distance of impulse and Markovain switching affect the stability for the system. Finally, two examples are provided to illustrate the effectiveness of the results proposed.
MSC:
| 93D23 | Exponential stability |
| 93E15 | Stochastic stability in control theory |
| 93C23 | Control/observation systems governed by functional-differential equations |
| 34K40 | Neutral functional-differential equations |
| 34K45 | Functional-differential equations with impulses |
| 34K50 | Stochastic functional-differential equations |
Keywords:
delay; exponential stability; impulsive; Markovian switching; neutral; Razumikhin technique; stochastic functional differential equationsReferences:
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