This article proposes a new technique for the tuning of a discrete adaptive controller that is designed based on Lyapunov stability concepts. The tuning is based on the minimisation of a performance index that can be calculated from a generalised eigenvalue problem (GEVP) using LMI's (Linear Matrix Inequalities). The proposed technique results in an adaptive controller with time-varying tuning gains. The solution is based on an approximation of the optimal dual adaptive control problem. The tuning technique was used to perform on-line control of a first-order system and an isothermal and a non-isothermal CSTR. The results show that the proposed approach provides better performance than an adaptive algorithm with the same structure, but with constant adaptation gains. Also, the proposed algorithm is shown to be superior to an adaptive controller based on a Recursive Least Squares (RLS) estimator during sudden changes in model parameters.