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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 10, pp. 1434–1440, October, 2006.
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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 Math J 58, 1626–1634 (2006). https://doi.org/10.1007/s11253-006-0158-6
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DOI: https://doi.org/10.1007/s11253-006-0158-6