Abstract: In this paper,the existent conditions of the solutions to LQ inverse problem are analysed so as to choose the desired closed loop poles,which become a set of optimal poles.A new design method for optimal control systems is presented based on the analysis of the LQ inverse problem for discrete time systems.The analytical relationship among the coefficients of open loop and closed loop characteristic polynomials and the weighting matrices is obtained.Given a set of desired closed loop poles,the weighting matrices Q and R are at once determined corresponding to these poles,and an optimal control system is obtained with prescribed poles.