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This paper deals with the problem of LZ disturbance attenuation for Hamiltonian systems. We first show that the L2 gain from the disturbance to a penalty signal may be reduced to any given level if the penalty signal is defined properly. Then, an adaptive version of the controller will be presented to compensate .the parameter perturbation. An adaptive Lz controller for the power system is designed using the proposed method and a simulation result with the proposed controller is given.A powerful design technique for stabilization of nonlinear systems is passivity-based control (PBC) [l]. In the PBC framework, the controller design proceeds along two stages. The first stage is to render passive a map with a suitably defined storage function, and the second stage is to perform an output feedback. For mechanical systems the design process has a physical meaning, e.g. the first stage can be carried out by shaping the potential energy of the system in such a way that the new potential energy function has a strict local minimum at the desired equilibrium, and the second stage is nothing but damping injection. Recently, the design technology has been extended to a broader class of systems described by port-controlled Hamiltonian (PCH) ~~ ~~

This paper deals with the problem of L2 disturbance attenuation for Hamiltonian systems. We first show that the L2 gain from the disturbance to a penalty signal may be reduced to any given level if the penalty signal is defined properly. Then, an adaptive version of the controller will be presented to compensate the parameter perturbation. When the perturbed parameters satisfy a suitable matching condition, it is easy to introduce the adaptive mechanism to the controller. Another contribution of this paper is to apply the proposed method to the excitation control problem for power systems. An adaptive L2 controller for the power system is designed using the proposed method and a simulation result with the proposed controller is given.

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