Abstract:In this paper,optimal control problem of time-delay digital control system has been studied using discrete orthogonal polynomials. The relationship between the state coefficient vector and control coefficient vector is obtained. The discrete orthogonal polynomials are used to modify the optimal equations into a set of linear algebraic ones for the approximate solutions of optimal state and control variables. Finally,a practical example is given by using discrete Chebyshev polynomial,discrete Laguerre polynomial and discrete Legendre polynomial,and the results obtained are satisfactoy.