Impulsive control of nonlinear systems with time-varying delays

A whole impulsive control scheme of nonlinear systems withtime-varying delays, which is an extension for impulsive control ofnonlinear systems without time delay, is presented in this paper.Utilizing the Lyapunov functions and the impulsive-type comparisonprinciples, we establish a series of different conditions underwhich impulsively controlled nonlinear systems with time-varyingdelays are asymptotically stable. Then we estimate upper bounds ofimpulse interval and time-varying delays for asymptotically stablecontrol. Finally a numerical example is given to illustrate theeffectiveness of the method.