Aiming at the problems that the exponentially variable gain Iterative Learning Control (ILC) algorithm is difficult to be further improved and lacks optimization theory,a control gain optimization method of exponentially variable gain Iterative Learning Control (ILC) algorithm in Linear Time-Invariant (LTI) systems is proposed.Firstly,the necessary and sufficient conditions for convergence in Single-Input Single-Output (SISO) discrete LTI systems are obtained from the Toeplitz matrix properties and matrix iteration theory,and the convergence of the algorithm is proved.Secondly,the monotonic convergence condition of the algorithm is obtained from the optimization theory.Finally,the exact solution of the optimal control gain is obtained,and the relationship between the exponential gain and the optimal control gain is obtained.The method obtains the optimal control strategy according to the state equation of the system,and can calculate the precise optimal control value,which further improves the system convergence speed.The simulation results show that the method can effectively improve the learning speed of the algorithm and has good control performance.