On the controllability of a nonlinear control system (Q1078125)

Nonlinear, time-invariant, finite-dimensional control systems are considered. Sufficient conditions for local controllability and global complete controllability are formulated. In the special case of a linear, finite-dimensional, time-invariant control systems these conditions are also necessary. The relationships among controllability, stability and optimality are investigated. The results presented in the paper offer another method for determining controllability of nonlinear systems. This method essentially differs from the differential-geometric approach [see e.g. \textit{H. Hermes}, SIAM J. Control. 12, 252-261 (1974; Zbl 0255.93005)].