Geodesic
STABILITY AND STABILIZATION OF IMPULSIVE AND SWITCHED HYBRID STOCHASTIC DELAY SYSTEMS
Liu, Jun1 ; Liu, Xinzhi1 ; Xie, Wei-Chau2
1 Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
2 Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 4, p. 315-341.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.004.04.09
Classification : 93C30, 34K35, 93E15
Keywords: Switched system, impulsive system, hybrid system, delay system, stochastic system, exponential stability, impulsive stabilization, Lyapunov-Razumikhin method.

Liu, Jun 1 ; Liu, Xinzhi 1 ; Xie, Wei-Chau 2

1 Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
2 Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada 
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Liu, Jun; Liu, Xinzhi; Xie, Wei-Chau. STABILITY AND STABILIZATION OF IMPULSIVE AND SWITCHED HYBRID STOCHASTIC DELAY SYSTEMS. Journal of nonlinear sciences and its applications, Tome 4 (2011) no. 4, p. 315-341. doi : 10.22436/jnsa.004.04.09. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.004.04.09/

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