# Necessary condition for the stabilizability of nonlinear systems with respect to a part of variables in the class of discontinuous controls

### 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.
Published

25.10.2006

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 58, no. 10, Oct. 2006, pp. 1434–1440, https://umj.imath.kiev.ua/index.php/umj/article/view/3544.

Issue

Section

Short communications