Impulsive stabilization of delay differential systems via the Lyapunov-Razumikhin method. (English) Zbl 1159.34347

The authors study the stability of nonlinear impulsive delay differential systems in the form \[ x'(t)=F(t,x_t),\;t\not=t_k;\quad \Delta x(t_k)=I_k(t_k, x_{t_k^-}),\;k\in\mathbb{N}; \quad x_{t_0}=\phi. \] 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.


34K20 Stability theory of functional-differential equations
34K45 Functional-differential equations with impulses
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