A fractional order composite MRAC for multi variable systems based on LDU factorization of Kp

By utilizing LDU factorization of high frequency gain (HFG) Kp, a novel fractional order composite model reference adaptive control (MRAC) is investigated for a class of fractional order multi variable systems. Firstly, in the proposed method, the stringent symmetry assumption related with the plant high frequency gain matrix is removed. Besides, by means of fractional order tracking differentiator, the parameter estimation errors is obtained to construct the fractional order parameter updating laws, which can improve the tracking performance and reduce the control cost. In addition, by utilizing indirect Lyapunov approach, the convergence of closed-loop control systems and parameters estimation are proved. Finally, for the purpose of showing the effectiveness of the proposed method, a numerical example are developed.