Input-to-state stability for a class of hybrid dynamical systems via hybrid time approach

Abstract

Abstract-This paper studies the ISS (input-to-state stability) for a class of HDS (hybrid dynamical systems). By using the concept of hybrid time for HDS, two kinds of ISS notions are proposed. They are called the first ISS property and the second ISS property of HDS. By employing the ISS properties on continuous and/or discrete dynamics in the HDS, the first and second ISS properties for the whole HDS are investigated. We show that there exists the first ISS property for the whole HDS if any one of dynamics in the HDS has the ISS property and the dwell time on this dynamics is sufficiently long even if there is no ISS property for the other dynamics. Moreover, the second ISS property of HDS is derived for the cases in which one kind of dynamics without external inputs has a stability property while the other one has no stability and ISS properties. Finally, one example is given for illustration.

Optimal control with stabilization for a class of hybrid dynamical systems

“…More recently, in [39][40], we formulated a class of more general HDS and obtained the related stability criteria. In this paper, we study the optimal control with stabilization for the HDS proposed in [39][40] with respect to the hybrid performance functional (HPF). The optimization problem for switched systems and impulsive systems has been received considerable attention lately (see [22][23][24][25][26][27][28][29][30][31]) because in many practical problems optimality of an associated cost performance functional is very practically important to system.…”

“…Most of the previously known works on stability in the literature on HDS focuses on switched systems, impulsive systems, and switched impulsive systems, see [32][33][34][35][36][37][38][39][40] and the references therein. More recently, in [39][40], we formulated a class of more general HDS and obtained the related stability criteria. In this paper, we study the optimal control with stabilization for the HDS proposed in [39][40] with respect to the hybrid performance functional (HPF).…”