The dynamics of many physical systems can be suitably described as the form of port-controlled Hamiltonian systems. Based on this, a number of control design methods have been successfully proposed and applied in both mechanical and electrical systems. However, the rigorous structure requirements of the classical Hamilton system inevitably limit its scope of application, with the multi-machine power system considering transfer conductances as one notorious example. This study presents the pseudo-generalised Hamiltonian system, which has a more general form and a wider range of application. A new Lyapunov candidate function is proposed and proved to be a real Lyapunov function under some assumptions. Two global centralised excitation control strategies are designed by a damping injection energy balancing method and the L 2 -disturbance attenuation method, respectively. Furthermore, a multi-machine power system with transfer conductance is taken as an example to explicitly describe the application of the proposed theory. Experimental results demonstrate the effectiveness of the methodology presented in this study.