Abstract
This paper presents a stable multivariable MRACS (Model Reference Adaptive Control System) including an estimator for unknown coefficients of polynomials which are the nondiagonal elements of the interactor matrix of the plant. It is shown that the degrees of the polynomials are bounded by the plant's degree and that there exists an identification model which retaines the left-lower triangles structure of the interactor matrix. The former relates the number of the coefficients to be estimated and the latter plays a key role on the stability proof. Thereafter, the adaptive control system is designed on the assumption of knowing degrees of diagonal elements of the interactor matrix. It is a most general extention of MRACS from the scalar system to the multivariable system in the sence that it requires the minimal restriction on the plant's transfer function and the minimal information on the plant's interactor matrix. The global stability of the total control system is proved through modification of the established method by Goodwin et al.. Some numerical examples are also presented to show the effectiveness of the proposed adaptive control in comparison with the ordinary adaptive control in which the interactor matrix should be completely known a priori.
