With the development of power system interconnection, low-frequency oscillation is becoming more and more prominent, and may cause instability of power systems. In this paper, two sources of uncertainty are modelled: plant and controller uncertainties. The non-linear dynamics of power systems under wide load variations are represented by a linear model with uncertainty in the form of a norm-bounded structure. The controller uncertainty resulting from resistor tolerance used in practical implementation is also represented by a norm-bounded model. This paper presents the design of resilient power system stabilizers (PSSs). The proposed PSS keeps stability against plant uncertainty and controller gain errors in the form of a linear matrix inequality (LMI)-sufficient condition. In addition to robust stability, the PSS design achieves regional pole placement to control the settling time and damping ratio, and consequently achieves good dynamic performance. The simulation shows that the proposed PSS design is efficient using the power system model and can drastically improve the dynamic performance of a single machine and a multi-machine power system.