Stability of sets of hybrid dynamical systems with aftereffect

Abstract

Abstract In the first part of the paper a family of hybrid systems with aftereffect is considered. For such equations, some results of the analysis of a set of trajectories based on matrix-valued functions defined on the product of spaces are given. In the second part of the paper, for the first time, uncertain sets of equations under impulsive perturbations are investigated. Estimates for the distance between extremal sets of trajectories are derived for the systems under consideration. In addition, conditions for the global existence of the sets of solutions regularized with respect to the parameter of uncertainty are proved.