STABILITY AND STABILIZATION OF IMPULSIVE AND SWITCHED HYBRID STOCHASTIC DELAY SYSTEMS
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Authors
Jun Liu
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Xinzhi Liu
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Wei-Chau Xie
- Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Abstract
Stability analysis is performed and stabilization strategies are proposed for a general class of stochastic delay differential equations subjected
to switching and impulses. Hybrid switching and impulses are combined to
exponentially stabilize an otherwise unstable stochastic delay system. Three
differential stabilization strategies are proposed, i.e. the average dwellime
approach, the impulsive stabilization, and a combined strategy. Both moment
stability and almost sure stability of the resulting impulsive and switched hybrid stochastic delay systems are investigated using the well-known Lyapunov-
Razumikhin method in the hybrid and stochastic setting. Several examples are
presented to illustrate the main results and numerical simulations are presented
to demonstrate the analytical results.
Share and Cite
ISRP Style
Jun Liu, Xinzhi Liu, Wei-Chau Xie, STABILITY AND STABILIZATION OF IMPULSIVE AND SWITCHED HYBRID STOCHASTIC DELAY SYSTEMS, Journal of Nonlinear Sciences and Applications, 4 (2011), no. 4, 315--341
AMA Style
Liu Jun, Liu Xinzhi, Xie Wei-Chau, STABILITY AND STABILIZATION OF IMPULSIVE AND SWITCHED HYBRID STOCHASTIC DELAY SYSTEMS. J. Nonlinear Sci. Appl. (2011); 4(4):315--341
Chicago/Turabian Style
Liu, Jun, Liu, Xinzhi, Xie, Wei-Chau. "STABILITY AND STABILIZATION OF IMPULSIVE AND SWITCHED HYBRID STOCHASTIC DELAY SYSTEMS." Journal of Nonlinear Sciences and Applications, 4, no. 4 (2011): 315--341
Keywords
- Switched system
- impulsive system
- hybrid system
- delay system
- stochastic system
- exponential stability
- impulsive stabilization
- Lyapunov-Razumikhin method.
MSC
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