Stability and L2-gain analysis for impulsive delay systems : an impulse-time-dependent discretized Lyapunov functional method

The problems of exponential stability and L2-gain for a class of time-delay systems with impulsive effects are studied. The main tool used is the construction of an impulse-time-dependent complete Lyapunov functional. By dividing the impulse interval and delay interval into several segments, the matrix functions of this functional are chosen to be continuous piecewise linear. Moreover, an impulse-time-dependent weighting factor is introduced to coordinate the dynamical behavior of the nondelayed and integral terms of this functional along the trajectories of the system. By applying this functional, delay-dependent sufficient conditions for exponential stability and L2-gain are derived in terms of linear matrix inequalities. As by-products, new delay-independent sufficient conditions for the same problems are also derived. The efficiency of the proposed results is illustrated by numerical examples