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Zbl 1159.34347
Wang, Qing; Liu, Xinzhi
Impulsive stabilization of delay differential systems via the Lyapunov-Razumikhin method. (English)
[J] Appl. Math. Lett. 20, No. 8, 839-845 (2007). ISSN 0893-9659

The authors study the stability of nonlinear impulsive delay differential systems in the form $$ x'(t)=F(t,x_t),\ t\not=t_k;\quad \Delta x(t_k)=I_k(t_k, x_{t_k^-}),\ k\in\Bbb{N}; \quad x_{t_0}=\phi. $$ By employing the Razumikhin technique and the Lyapunov function method, they obtain sufficient conditions for the trivial solution to be globally exponentially stable. Criteria for the global exponential stability of a linear impulsive delay system are derived as applications. An example and its simulation are given to illustrate the results. This nice paper will be of interest to the researchers working on impulsive differential equations and on the stability theory.
[Qingkai Kong (DeKalb)]

MSC 2000:: *34K20 Stability theory of functional-differential equations
34K45 Equations with impulses

Keywords: Razumikhin technique; Lyapunov function; impulsive delay differential equations; global exponential stability

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