Asymptotic stability analysis and design of nonlinear impulsive control systems

In this work, the stability analysis and design problems are studied for a class of nonlinear impulsive control systems. Via the multi-comparison system, we establish a new comparison lemma that ensures asymptotic stability of impulsive differential systems. Based on that, we introduce vector Lyapunov functions to derive some efficient conditions and apply the results into the control design of a chaotic system. It is worth pointing out that the component Lyapunov functions need not be strictly positive definite. Necessary comparison shows that we obtain a larger stable region. Finally, some simulation results are presented to verify the derived conclusions.