Impulsive Control of Discrete Systems With Time Delay

This note deals with impulsive control of discrete systems with time delay. It´s the first time that an impulsive controller was introduced for discrete systems with time delay. Firstly, some stability criteria for delay discrete systems with impulse effects are obtained by using Lyapunov functionals and Razumikhin technique. These stability criteria show that if the impulses satisfy some conditions, then the original stable systems can keep their stability property even with impulse effects. Then by using Lyapunov functionals or Lyapunov functions together with Razumikhin technique, two stability criteria for the discrete systems with time delay under impulsive control are given. These two results show that unstable systems can be stable under impulsive control. Some examples are also presented to illustrate the efficiency of the obtained results.