This paper describes the design of robust power system stabilizers (PSS) for a single generator tie line (SGTL) power system. Unlike the conventional PSS design based on a single system operating point, the proposed method develops a more realistic approach by taking into account various uncertainties involved in power system operation and modelling such as disturbances, modelling errors, changes in the system parameters, system structure and operating conditions. This approach provides a technique for determining stabilizer transfer function for a region of power system operating points establishing a demarcation line between stable and unstable areas on the complex power plane. The Nevanlinna-Pick theory is applied to obtain the final transfer function. The design procedure is demonstrated for a system with typical parameters. Extensive simulation results are presented to confirm the superiority of the proposed PSS in comparison with a conventional PSS.