KL_*-stability for a class of hybrid dynamical systems. (29th July 2017) - Liu, Bin; Dam, Hai Huyen Heidi; Teo, Kok Lay; Hill, David John
Abstract: This article studies KL_* -stability (the stability expressed by KL_* -class function) for a class of hybrid dynamical systems (HDS). The notions of KL_*K_* -property and KL_* -stability are proposed for HDS with respect to the hybrid-event-time. The KL_* -stability, which is based on K or L property of the continuous flow, the discrete jump, and the event in an HDS, extends the KLL -stability and the event-stability reported in the literature for HDS. The relationships between KL_*K_* -property and KL_* -stability are established via introducing the hybrid dwell-time condition (HDT). The HDT generalizes the average dwell-time condition in the literature. For an HDS with KL_*K_* -property consisting of stabilizing L -property and destabilizing K -property, it is shown that there exists a common HDT under which the HDS will achieve KL_* -stability. Thus HDT may help to derive some easily tested conditions for HDS to achieve uniform asymptotic stability. Moreover, a criterion of KL_* -stability is derived by using the multiple Lyapunov-like functions. Examples are given to illustrate the obtained theoretical results.