For a single-machine, infinite-bus power system, digital robust stabilizers (controllers) are designed using modern H-infinity optimization. The objective is to design high-performance digital stabilizers with low cost in implementation on microprocessors; in particular, the digital stabilizers designed have low orders, require considerably slow sampling rates for implementation, and outperform the conventional (analogue) power system stabilizer on a series of dynamic performance tests. Four H-infinity, stabilizers are designed and investigated : (1) an analogue SISO stabilizer measuring the speed signal and then implemented digitally; (2) a SISO digital stabilizer designed in discrete time; (3) a multivariable digital stabilizer measuring both speed and power signals with a single sampling rate; (4) a multirate digital stabilizer involving two sampling rates and designed using recently developed multirate control theory. The importance of weighting functions is stressed in the design process.