The paper focuses on a robust decentralised excitation control of multimachine power systems. The authors are concerned with the design of a decentralised state feedback controller for the power system to enhance its transient stability and ensure a guaranteed level of performance when there exist variations of generator parameters due to changing load and/or network topology. It is shown that the power system can be modelled as a class of interconnected systems with uncertain parameters and interconnections. The authors develop a guaranteed cost control technique for the interconnected system using a linear matrix inequality (LMI) approach. A procedure is given for the minimisation of the cost by employing the powerful LMI tool. The proposed controller design is simulated for a three-machine power system example. Simulation results show that the decentralised guaranteed cost control greatly enhances the transient stability of the power system in the face of various operating points, faults in different locations or changing network parameters.