In this paper, the infinite-horizon optimal control problem with quadratic performance index in discrete-time multi-delay systems is addressed. The classical approach of using an augmented state space for single-delay systems is extended to the multi-delay case. The solvability conditions for the considered state-space representation are established and control system robustness to uncertainties is formally evaluated. The optimal solution is given in a state-feedback form with the design equations consistent with the standard ones for undelayed systems. Thus, the problem can be treated with the existing numerical algorithms and solver packages. The analytical findings are illustrated in a simulation scenario concerning optimal control of a logistic network.