An Impulsive Delay Inequality Involving Unbounded Time-Varying Delay and Applications

In this paper, a new impulsive delay inequality that involves unbounded and nondifferentiable time-varying delay is presented. As an application, some sufficient conditions ensuring stability and stabilization of impulsive systems with unbounded time-varying delay are derived. Some numerical examples are given to illustrate the results. Especially, a stabilizing memoryless controller for a second-order time-varying system with unbounded time-varying delay is proposed.