On the Dynamic Stability of Impulsive Mechanical Systems with Delay

Abstract

We consider impulsive mechanical systems with delay and establish sufficient conditions for asymptotic stability of the equilibrium positions of a system with periodic parameters in the linear approximation. It is also assumed that the value of delay is equal to the period of the system. The conditions of parametric stability of the lower equilibrium position of a mathematical pendulum are deduced with regard for the impulsive perturbations and delay.