Model Reference Adaptive Control of MIMO Systems in the Case When only Signs of Principal Leading Minors are Known as for High Frequency Gain Matrix

Abstract

In the paper a new direct MIMO adaptive controller with reduced prior knowledge of the high frequency gain matrix is proposed. At first, it is shown that for any nonsingular high frequency gain matrices K with nonzero principal leading minors, there exist a positive definite matrix K_P and a triangular matrix K_T such that K=K_pK_T. Next, a new direct model reference adaptive controller is developed by analyzing the derivative of a positive definite function including the positive definite matrix K_P. As for high frequency gain matrixes, only the signs of the principal leading minors are required in the developed controller. It is also proved that the output error becomes asymptotically stable even if there is not the persistency of excitation of the regressor vector.