Stability properties of nonlinear stochastic impulsive systems with time delay. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Alwan, Mohamad S.; Liu, Xinzhi; Xie, Wei-Chau
• Is Part Of: Stochastic analysis and applications. Volume 34:Issue 1(2016)
• Page Start: 117
• Page End: 136
• Publication Date: 2016-01-02
• Subjects: Stability -- stabilization -- Lyapunov–Razumikhin technique -- comparison principle -- time delay -- impulsive effects; 34K20; 34K34; 34K45; 34K50; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2015.1106951
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: 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.