On stabilization of nonlinear Hamiltonian systems and nonconservative systems in elasticity

For nonlinear Hamiltonian Systems using invariance principle sufficient conditions for local and global asymptotic stability and instability are derived. For the characterization of invariant sets needed to establish asymptotic stability conditions, certain results for the univalence of nonlinear maps are used. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained.