This paper describes a new structure for a stability-enhancing excitation controller designed using a nonlinear multimachine system model and Lyapunov's direct method. The controller is shown to be robust, as the damping it introduces into the system is insensitive to changes in both the system topology/parameters and the pattern of network flows. Each individual controller contributes positively to the overall system damping with no undesirable interaction between controllers. These features should allow a decentralised approach to the design of the AVR+PSS. Such a design approach is compatible with the new competitive market structures and should result in savings on commissioning costs. Simulation results for a multi-machine power system confirmed that the controllers are effective in damping local and inter-area power swings.