Multivariable MRAC using high frequency gain matrix factorization

A MIMO (multiple-input, multiple-output) analog to the well-known Lyapunov-based SISO (single-input, single-output) design of MRAC (model-reference adaptive control) has been recently introduced by L. Hsu et al. (2001). The new design utilizes a control parametrization derived from a factorization of the high-frequency gain matrix K_p =SDU, where S is symmetric positive-definite, D is diagonal and U is unity upper-triangular. Only the signs of the entries of D or, equivalently, the signs of the leading principal minors of K_p, were assumed to be known. However, the result was restricted to plants with (vector) relative degree one. In this paper, we extend the MRAC for more general plants with relative degree greater than one. We present three possible factorizations of K_p and the resulting update laws