This paper addresses a new robust control strategy to synthesis of robust proportional-integral-derivative (PID) based power system stabilisers (PSS). The PID based PSS design problem is reduced to find an optimal gain vector via an H1 static output feedback control (H1-SOF) technique, and the solution is easily carried out using a developed iterative linear matrix inequalities algorithm. To illustrate the developed approach, a real-time experiment has been performed for a longitudinal four-machine infinite-bus system using the Analog Power System Simulator at the Research Laboratory of the Kyushu Electric Power Company. The results of the proposed control strategy are compared with full-order H1 and conventional PSS designs. The robust PSS is shown to maintain the robust performance and minimise the effect of disturbances properly.