2017
Том 69
№ 9

All Issues

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.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 10, pp 1626-1634.

Citation Example: Kovalev A. M., Kravchenko N. V., Nespirnyi V. N. 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.

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