Stability Analysis of a Time-Delay Load Frequency Control System via an Improved Matrix-Separation-Based Inequality

This study focuses on the stability of time-delay load frequency control (LFC) systems. Based on the Lyapunov–Krasovskii (L–K) functional method, a stability criterion with less conservatism and lower computational complexity is proposed. Unlike recent methods that decrease conservatism through enhancing the complexity of L–K functional, only the double integral is augmented in this paper. To estimate the L–K functional derivatives more precisely, an improved matrix-separation-based inequality is proposed, which introduces some delay-derivative-dependent matrices rather than the high-dimensional free matrices. By applying the augmented L–K functional and the improved matrix-separation-based inequality, the stability criterion is established. Case analysis demonstrates that the new stability criterion has less conservatism and lower computational complexity, thereby validating the correctness of the method presented.