Stability properties of nonlinear stochastic impulsive systems with time delay

作者：Alwan Mohamad S^*; Liu Xinzhi; Xie Wei Chau

来源：Stochastic Analysis and Applications, 2016, 34(1): 117-136.

DOI：10.1080/07362994.2015.1106951

• Stability
• stabilization
• Lyapunov-Razumikhin technique
• comparison principle
• time delay
• impulsive effects
• 34K20
• 34K34
• 34K45
• 34K50

This article establishes mean square stability and stabilization for stochastic delay systems with impulses. Using Razumikhin methodology, two approaches, classical Lyapunov-based method and comparison principle, are proposed to develop sufficient conditions that guarantee the stability and stabilization properties. It is shown that if the continuous system is stable and the impulses are destabilizing, the impulses should not be applied frequently. On the other hand, if the continuous system is unstable, but the impulses are stabilizing, the impulses should occur frequently to compensate the continuous state growth. Numerical examples are also presented to clarify the proposed theoretical results.

• 出版日期2016-1-2