A technique is described for the design of linear multivariable systems in which the plant parameters are constant but unknown. These parameters are represented by random variables with known mean values and variances. A Wiener type of z-domain solution is derived to the resulting generalised linear quadratic optimal control problem. These results are also interpreted in the time domain, and the equivalent Kalman filtering solution is derived. To enable the controller to be applied in self-tuning control systems, the plant is represented in discrete polynomial form and a simple diophantine equation solution is also obtained.