Abstract and Applied Analysis
Volume 2009 (2009), Article ID 617936, 9 pages
doi:10.1155/2009/617936

Bounded motions of the dynamical systems described by differential inclusions

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.