On connectivity of the set of discontinuous solutions of a dynamic system with impulsive control (Q1390441)

A class of nonlinear control systems with impulsive integrally bounded controls is considered. The set of the admissible trajectories of a system from this class is defined as the closure of the set of all absolutely continuous trajectories of this system (in the topology of point-wise convergence). First, some topological properties of the set of admissible controls are established. Next, the connectivity of the corresponding attainability set is studied under suitable assumptions.