Abstract: The stability of Hamiltonian systems with time delay was investigated. Using the technique of the Lyapunov direct method and the dissipative structural properties of Hamiltonian systems, some sufficient conditions are derived for the stability of several classes of time-delay Hamiltonian systems. First, the stability is studied for the system with delay only in the Hamiltonian function, with which the stability of a class of time-delay nonlinear systems is also investigated by Hamiltonian realization. Second, the robust stability is considered for a class of time-delay Hamiltonian systems which possesse time-invariant uncertainties belonging to some convex bounded polytypic domain. Finally, several illustrative examples are studied by using the proposed results. Examples show that the results are very practicable in analyzing the stability of some classes of time-delay nonlinear systems.

Key words: time-delay nonlinear system , uncertainty, sufficient condition, robust stability, time-delay Hamiltonian system