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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.

MSC:

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