On K L∗-stability via hybrid-event-time for hybrid dynamical systems
This paper investigates K L<sub>*</sub>-stability for hybrid dynamical systems (HDS). The notions of K L <sub>θ</sub>K<sub>θK</sub>-property and K L <sub>θ</sub>-stability were proposed for HDS with respect to the hybrid-event-time. The K L <sub>θ</sub>-stability unifies the recently reported K L L-stability and event-stability for HDS. The relationships between K L <sub>θ</sub> K<sub>θK</sub>-property and K L <sub>θ</sub>-stability were established via introducing the K L <sub>θK→θL</sub>-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 <sub>θ</sub>-stability was derived by using the multiple Lyapunov-like functions.