Abstract: The convergence rate is analyzed for both D-type and P-type learning laws in linear time-invariant control system. A sufficient condition is given by the Frobenius norm and time-weighted norm to guarantee the convergence of D-type and P-type learning laws. Furthermore, the quantitative relation between iterative number and the relation between convergence rate and constraint condition are given. Simultaneously, the approach to choosing the gain matrix for D-type/P-type learning law so as to get highest convergence rates is given by gradient flow and the property of Frobenius norm. Numerical simulation shows the effectiveness of the proposed method.