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New Razumikhin-type theorems on the stability for impulsive functional differential systems. (English) Zbl 1120.34056

Some new Lyapunov functions technique is applied to the impulsive nonlinear functional differential equation \[ \begin{cases} x'(t)=f(t,x_t),&t\not= \tau_k,\\ x(t)=x(t^-)+I_k (x(t^-)),&t=\tau_k. \end{cases} \] Several interesting examples are given to show the advantages of results obtained in the paper.

MSC:

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