Multivariable model reference adaptive control without constraints on the high-frequency gain matrix

Stability is improved for a multivariable model reference adaptive control algorithm when the high-frequency gain matrix is unknown. Only an upper bound on the norm of the matrix is required. A transformation of the parameters, with a sort of `hysteresis´, is used to guarantee that a controller matrix, which is nominally the inverse of the high-frequency gain matrix, remains nonsingular. It is shown that all the signals in the adaptive system are bounded and that the tracking error and the regressor error converge to zero for all bounded reference inputs. Furthermore, exponential convergence is achieved when the regressor vector is persistently exciting