Stability for hybrid event systems

This paper studies the stability of hybrid event systems (HES). By the partition of time set, we formulate the HES model which includes several special cases reported in the literature. Two types of stability notions (the first and the second stability) are proposed to reflect the effect on stability from hybrid events. A new stability analysis method called hybrid-event-time Lyapunov function (HTLF) approach is proposed for HES. A basic stability result is derived for HES. That is: a HES has the second asymptotic stability if and only if there exists a HTLF which is strictly decreasing and converges to zero. Moreover, by constructing HTLF and integrating the Razumikhin technique, the backward and forward HTLF-Razumikhin-type stability theorems are established. As applications, the results are then used to derive Razumikhin-type exponential stability theorems for impulsive HES with delays. Finally, one example is given to illustrate the results.