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

This paper investigates the problems of robust stability, stabilization and H ∞ -control for uncertain impulsive systems with time-delay. The parametric uncertainties are assumed to be time-varying and norm-bounded. Three classes of impulsive systems with time-delay are considered: the systems with stable/stabilizable continuous dynamics and unstable/unstabilizable discrete dynamics, the systems with unstable/unstabilizable continuous dynamics and stable/stabilizable discrete dynamics, and the systems where both the continuous-time dynamics and the discrete-time dynamics are stable/stabilizable. For each class of system, by using the Lyapunov function and Razumikhin-type techniques, sufficient conditions for robust stability, stabilization and H ∞ -control are developed in terms of linear matrix inequalities. Numerical examples are given which illustrate the applicability of the theoretical results.