This article introduces a new design of a decentralized robust optimal feedback controller for a class of large-scale systems using the modified algebraic Riccati equations. The studied class of large-scale systems is characterized by structured uncertainties that are bounded. Our main contribution in this work is the use of the Lyapunov direct method for the stability analysis, associated with a quadratic function, in order to determine a new sufficient condition to guarantee the global asymptotic stability of the class of the studied uncertain interconnected systems. The proposed control approach is then implemented on a large-scale power systems composed of three interconnected generators. Simulation results show that the proposed robust optimal controller is quite effective and has an outstanding performance.