Finite-time control of singular nonlinear time-delay systems via Hamiltonian method

In this article, we study the finite time control problem for a nonlinear singular delay Hamiltonian system. First, the general nonlinear singular Hamiltonian system with delay is transformed into its equivalent Hamiltonian form. Then, through a designed state feedback controller, we obtain its strictly dissipative Hamiltonian form. The appropriate Hamiltonian function and Lyapunov function are selected to study the finite time stability of the dissipative Hamiltonian system. The paper presents a stability result on the delay system. It should be pointed out that, due to the existence of delay term, it is more difficult on the stability analysis for the singular system.