Copyright © 2009 Nihal Ege and Khalik G. Guseinov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The boundedness of the motions of the dynamical system described by a differential inclusion with control vector is studied. It is assumed that the right-hand side of the differential inclusion is upper semicontinuous. Using positionally weakly invariant sets, sufficient conditions for boundedness of the motions of a dynamical system are given. These conditions have infinitesimal form and are expressed by the Hamiltonian of the dynamical system.