Kovalev A. M.
Necessary condition for the stabilizability of nonlinear systems with respect to a part of variables in the class of discontinuous controls
Ukr. Mat. Zh. - 2006. - 58, № 10. - pp. 1434–1440
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.
Berezansky Yu. M., Kharlamov P. V., Khruslov E. Ya., Kit G. S., Korneichuk N. P., Korolyuk V. S., Kovalev A. M., Kovalevskii A. A., Lukovsky I. O., Mitropolskiy Yu. A., Samoilenko A. M., Savchenko O. Ya.
Ukr. Mat. Zh. - 2000. - 52, № 11. - pp. 1443-1445
Ukr. Mat. Zh. - 1995. - 47, № 2. - pp. 186–193
We prove the theorem on necessary and sufficient conditions of partial instability and the theorem on partial stabilization of nonlinear dynamical systems. We obtain sufficient conditions of controllability for systems linear with respect to control. We also study the problem of control and stabilization of an angular motion of a solid body by rotors.