Necessary condition for the stabilizability of nonlinear systems with respect to a part of variables in the class of discontinuous controls - Kovalev, A. M.; Kravchenko, N. V.; Nespirnyi, V. N. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
We investigate the problem of the existence of a discontinuous feedback that guarantees the stabilization of a nonlinear control system with respect to a part of variables. A solution of the system is defined in the Filippov sense. We establish a necessary condition for stabilization with respect to a part of variables in the class of discontinuous controls, which generalizes the Ryan condition to the case of stabilization with respect to a part of variables. An example of a mechanical system that cannot be stabilized with respect to a part of variables is considered.