Delay-dependent stability and hybrid L2 X l2-gain analysis of linear impulsive time-delay systems : a continuous timer-dependent Lyapunov-like functional approach

This paper presents a new approach for analyzing delay-dependent stability and hybrid L2 X l2-gain performance of linear impulsive delay systems. The new approach is inspired by the delay-partitioning method, the timer-dependent Lyapunov functional method, and the looped-functional method. In the delay-partitioning framework, a new type of timer-dependent Lyapunov functional is constructed, which depends on the partition on impulse intervals and also on impulse dynamics. Different from the previous discontinuous Lyapunov functionals, the introduced Lyapunov functional is continuous along the trajectories of the considered impulsive delay system. Consequently, two different problems of exponential stability and hybrid L2 X l2-gain performance are tackled by using the same class of Lyapunov functionals. It is shown that the positive definiteness of this Lyapunov functional inside impulse intervals is not necessary for proving exponential stability. By use of new integral inequalities based techniques, delay-dependent criteria for exponential stability and finite hybrid L2 X l2-gain are established in terms of linear matrix inequalities. Numerical examples are provided to illustrate the efficiency of the new approach.