TY - GEN
T1 - Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation
AU - Maschke, Bernard M.J.
AU - Ortega, Romeo
AU - van der Schaft, Arjan J.
N1 - Conference code: 37
PY - 1998/12/16
Y1 - 1998/12/16
N2 - We propose a constructive procedure to modify the total energy function of forced Hamiltonian systems with dissipation in order to generate Lyapunov functions for non-zero equilibria. A key step in the procedure, which is motivated from energy-balance considerations standard in network modeling of physical systems, is to embed the system into a larger Hamiltonian system for which a series of Casimir functions (i.e., first integrals) can be easily constructed. For linear systems the resulting Lyapunov function is the incremental energy, thus our derivations provide a physical explanation to it. An easily verifiable necessary and sufficient condition for the applicability of the technique in the general nonlinear case is given. Some examples that illustrate the method are given.
AB - We propose a constructive procedure to modify the total energy function of forced Hamiltonian systems with dissipation in order to generate Lyapunov functions for non-zero equilibria. A key step in the procedure, which is motivated from energy-balance considerations standard in network modeling of physical systems, is to embed the system into a larger Hamiltonian system for which a series of Casimir functions (i.e., first integrals) can be easily constructed. For linear systems the resulting Lyapunov function is the incremental energy, thus our derivations provide a physical explanation to it. An easily verifiable necessary and sufficient condition for the applicability of the technique in the general nonlinear case is given. Some examples that illustrate the method are given.
U2 - 10.1109/CDC.1998.761738
DO - 10.1109/CDC.1998.761738
M3 - Conference contribution
SN - 0-7803-4394-8
T3 - IEEE Conference on Decision and Control, CDC
SP - 3599
EP - 3604
BT - Proceedings 37th IEEE Conference on Decision and Control, CDC 1998
PB - IEEE
CY - Los Alamitos, CA
T2 - 37th IEEE Conference on Decision and Control, CDC 1998
Y2 - 16 December 1998 through 18 December 1998
ER -