AH∞self-tuning controller which is based on the generalizedH∞cost-function is described that includes robust design features. TheGH∞control law is simple to compute and is suitable for multivariable self-tuning control applications. The simplifications achieved in the controller structure which are necessary for use in self-tuning, depend upon the assumptions made on system and cost-weighting models. The cost-function weights are assumed to ensure a system matrix can be factorized into a particular form. The control law is coupled to an extended least squares identification algorithm. TheGH∞control law may be designed to be insensitive to unmodelled dynamics and the self-tuning action provides adaption to parametric uncertainty.