On K L∗-stability via hybrid-event-time for hybrid dynamical systems

This paper investigates K L ∗-stability for hybrid dynamical systems (HDS). The notions of K L θKθK-property and K L θ-stability were proposed for HDS with respect to the hybrid-event-time. The K L θ-stability unifies the recently reported K L L-stability and event-stability for HDS. The relationships between K L θ KθK-property and K L θ-stability were established via introducing the K L θK→θL-condition with the hybrid dwell-time condition (HDT). The HDT generalized and unified the often used average dwell-time condition (ADT) and the converse-ADT in the literature for the stability of HDS. Finally, a criterion of K L θ-stability was derived by using the multiple Lyapunov-like functions.