Stabilization analysis of time-varying Hamiltonian systems with input delay

The stabilization problem of time-varying port-controlled Hamiltonian (PCH) systems with input delay is addressed in this paper. Based on energy-shaping approach and using Lyapunov-Krasovskii (L-K) functional theorem, a feedback controller is proposed for the asymptotical stability of the closed-loop system in presence of delay. Like Casimir function is proposed to help shaping the Hamiltonian as a candidate of Lyapunov function in the extended systems. A numerical example is presented to illustrate the effectiveness of the results obtained in this paper.