On connectivity of the set of discontinuous solutions of a dynamic system with impulsive control. (English. Russian original) Zbl 0916.93013

Russ. Math. 40, No. 11, 85-93 (1996); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1996, No. 11 (414), 82-89 (1996).
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.


93B03 Attainable sets, reachability
93C10 Nonlinear systems in control theory