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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 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 , are assumed known.Index Terms-Direct adaptive control, high-frequency gain, matrix factorization, model reference adaptive control (MRAC), multiple-input-multiple-output (MIMO) systems.

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