Multivariable adaptive control using high-frequency gain matrix factorization

In this note, we extend the application of a less restrictive condition about the high-frequency gain matrix to design stable direct model reference adaptive control for a class of multivariable plants with relative degree greater than one. The new approach is based on a control parametrization derived from a factorization of the high-frequency gain matrix K_p in the form of a product of three matrices, one of them being diagonal. Three possible factorizations are presented. Only the signs of the diagonal factor or, equivalently, the signs of the leading principal minors of K_p, are assumed known.