On the construction of an asymptotic analog of a pencil of trajectories for a linear system with a single-impulse control
In the paper linear, finite-dimensional, time dependent control systems described by an ordinary differential state equation are considered. The main purpose of the paper is to discuss the behaviour of the control systems with impulsive controls and with impulsive constraints. Using the methods taken directly from differential geometry and mathematical analysis the properties of the solutions are investigated in detail. Many properties of a pencil of the system trajectories are pointed out. Moreover, many remarks and comments concerning so-called attraction sets are given. A simple numerical example illustrates the theoretical considerations. Finally, it should be stressed, that similar problems have been widely considered in the monograph [\textit{A. G. Chentsov}, ``Asymptotic attainability'' (Mathematics and its Applications 383, Dordrecht: Kluwer) (1997; Zbl 0859.93002)].
scientific article; zbMATH DE number 2170251