Model reference adaptive control of multivariable plants with unknown interactor matrix

A stable model reference adaptive control (MRAC) scheme is presented for multivariable plants with unknown interactor matrix. A new parametrization of the controller structure is developed by using the knowledge of only the upper bound on the maximum degree of the interactive matrix of the plant transfer matrix. A modified estimation error is introduced in the adaptive law for updating the controller parameters. By estimating a set of extra parameters and projecting some of the estimated parameters onto a certain region in the parameter space, the MRAC scheme guarantees that all signals in the adaptive system are uniformly bounded and the tracking error goes to zero asymptotically with time. A complete stability analysis is given based on a unified theoretical framework