Estimation of an optimal controller is a fundamental problem in control engineering and is widely known as Optimization. Numerous computation and numerical techniques have been evolved during the past years for the estimation of the optimal solution. Optimal control of a discrete-time system is concerned with optimizing a given objective function using "Homogenous Polynomial Lyapunov Function (HPLF)". This research focuses upon the design of optimal Guaranteed Cost Controller (GCC) for discrete-time uncertain system using HPLF. The uncertainties are assumed to be norm-bounded uncertainties. The effect of actuator saturation is also incorporated in the system. Sufficient conditions for the existence of HPLF are derived in terms of Linear Matrix Inequalities (LMI). The LMI approach has the advantage that it can be solved efficiently using Convex Optimization. LMI's combined with HPLF helps to design the guaranteed cost controller which minimizes the cost by minimizing cost function. Furthermore, the state trajectories and the invariant set are also shown for the observation of the overall performance. (C) 2016 Sharif University of Technology. All rights reserved.