Stability analysis of aperiodic impulsive delay systems using sum of squares approach

Abstract

The stability problem of aperiodic impulsive delay systems with unstable continuous and discrete dynamics is addressed in this article. New delay-dependent stability conditions are proposed by employing a clock-dependent Lyapunov–Krasovskii-like functional composed of a Lyapunov–Krasovskii functional and a high-order polynomial matrix function. The stability conditions are then solved using sum of squares programming techniques, yielding less conservative results than the looped-functionals approach. Finally, the simulation results demonstrate the effectiveness of the results.