An impulsive delay differential inequality and applications

An impulsive delay differential inequality is formulated in this paper. An estimate of the rate of decay of solutions to this inequality is obtained. It can be applied to the study of dynamical behavior of delay differential equations from the impulsive control point of view. As an application, we consider a class of impulsive control systems with time-varying delays and establish a sufficient condition to guarantee the global exponential stability. It is shown that, via proper impulsive control law, a linear delay differential system can be exponentially stabilized even if it is initially unstable. A numerical example is given to demonstrate the effectiveness of the development method.