Adaptive H∞ control of time-delay Hamiltonian systems with parametric uncertainties and disturbances

This paper addresses the adaptive H∞ control problem for a class of time-varying delay Hamiltonian systems with uncertainties and unknown disturbances. The uncertainties under consideration are some small parameter perturbations involved in the structure of the Hamiltonian system. In order to construct an adaptive H∞ controller, the case that there is no perturbations in the system are studied firstly and a controller is designed which ensure the asymptotic stability and the L2 gain performance of the resulted closed-loop system. Then the adaptive H∞ control problem is solved under some sufficient conditions. It is shown that the control law with desired L2 gain from the disturbance to a penalty signal can be obtained by using the Lyapunov-Krasovskii method. Finally, an example is given to demonstrate the proposed results.