Some sufficient conditions for asymptotic stability of impulsive control systems with impulses at fixed times were recently presented. In this note, we derive some less conservative conditions for asymptotic stability of such impulsive control systems and the results are used to design impulsive control for a class of nonlinear systems. The class of nonlinear systems considered is also enlarged.

Abstract-This paper considers the stabilization and synchronization of Chua's oscillators via an impulsive control with time-varying impulse intervals. Some less conservative conditions were derived in the sense that the Lyapunov function is only required to be nonincreasing along a subsequence of the switchings.

In this note, one state transformation is used to construct switching laws for a class of switched systems totally composed of unstable subsystems. Some sufficient conditions for determining the switching law, such that the system is asymptotically stable, are derived.

In this note, we analyze the discrete behavior to identify all kinds of cycles of hybrid nonlinear systems and then study the continuous behavior along each kind of cycle. Based on these analysis, we construct some continuous functions to bound Lyapunov functions along all subsystems and identify a subsequence of time points where the Lyapunov functions are nonincreasing. We use these results to derive some new sufficient conditions for the robust stability of a class of hybrid nonlinear systems with polytopic uncertainties. These conditions do not require the Lyapunov functions to be nonincreasing along each subsystem nor the whole sequence of the switchings. Furthermore, they do not require the knowledge of continuous trajectory.Index Terms-Hybrid nonlinear systems, robust stability.

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