Estimate of finite-time domain of attraction for a class of nonlinear Hamiltonian systems with time delay

This paper investigates the finite-time stability (FTS) and the estimate of finite-time domain of attraction for a class of nonlinear time-delay Hamiltonian systems via Lyapunov-Krasovskii (L-K) functional method, and proposes some delay-dependent results on the issues. Firstly, a time-varying criterion on the FTS is proposed for general nonlinear time-delay systems via L-K functional approach. Then, based on the criterion, a delay-dependent condition on the FTS is derived for the nonlinear time-delay Hamiltonian systems by constructing a specific L-K functional. Thirdly, we use the obtained FTS result to investigate the estimate of finite-time domain of attraction problem, and present an estimate result for the Hamiltonian systems. Finally, the study of an illustrative example shows that the results obtained in this paper work very well in the estimate of finite-time domain of attraction of some nonlinear time-delay (Hamiltonian) systems.