2019
Том 71
№ 10

All Issues

Nespirnyi V. N.

Articles: 1
Brief Communications (Russian)

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.

↓ Abstract   |   Full text (.pdf)

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.