Robust stability of uncertain impulsive control systems with time-varying delay

In this paper, we are concerned with the robust stability problem of an uncertain impulsive control system with time-varying delay. By employing the formula for the variation of parameters and estimating the Cauchy matrix, several criteria on robust exponential stability are derived and the exponential convergence rate is estimated. Based on $P$-norm and $P$-measure of matrix, it is seen that our sufficient conditions are less restrictive than the ones in the earlier publication. Some numerical examples and simulations are given to illustrate the theoretical results and to show that the criteria can be applied to stabilize the unstable continuous system with time delays and uncertainties by utilizing impulsive control.