In the realm of modern interconnected systems, achieving stability represents a pivotal challenge due to the complex dynamics among various components. This paper presents a new approach to stability analysis, leveraging linear matrix inequalities and Lyapunov-Krasovskii functionals. The framework of memory-based coupling sampled data control is enhanced by a quantum genetic algorithm. By incorporating linear matrix inequality approach, this study establishes a robust mathematical foundation for characterizing stability conditions and synthesizing control gains. This innovative integration provides a powerful toolset to optimize control parameters while mitigating the impact of disturbances. The simulation findings are explicitly based on experimental values of two-area interconnected power systems with doubly fed induction generator based wind farm, which guarantees the asymptotic stability of the proposed controller.