Sufficient conditions for the stable controllability of a nonautonomous system in the critical case (Q1776245)

Nonlinear, finite-dimensional, nonautonomous control systems described by ordinary differential state equations are considered. The stable local controllability in a given finite time interval is defined and studied in detail. It is generally assumed that the values of controls are taken from a given set. Using the notions of different kinds of attainable sets, sufficient conditions for the stable controllability are formulated and proved. In the proofs of the main theorems methods of differential geometry and mathematical analysis are extensively used. The efficiency of a given controllability condition is illustrated by two simple numerical examples. Moreover, many remarks and comments on controllability problems for nonlinear control systems are presented. Finally, it should be pointed out that similar problems have been considered in the monograph [\textit{J. Klamka}, Controllability of dynamical systems (Mathematics and its Applications: East European Series 48, Dordrecht: Kluwer) (1991; Zbl 0732.93008)].