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.
"Bounded Motions of the Dynamical Systems Described by Differential Inclusions." Abstr. Appl. Anal. 2009 1 - 9, 2009. https://doi.org/10.1155/2009/617936