Abstract:
A system of ordinary differential equations with
impulse action at fixed moments of time
is considered. The system is assumed to have the zero solution.
It is shown that the existence of a corresponding Lyapunov function
is a necessary and sufficient condition for the uniform asymptotic stability of the zero solution. Restrictions on perturbations of the right-hand sides of
differential equations and impulse actions are obtained under which
the uniform asymptotic stability of the zero solution of
the “unperturbed” system implies the uniform asymptotic
stability of the zero solution of the “perturbed” system.