Robust Stability and Observability Analysis of Transmission Line

This work focuses on the analysis of uncertain neutral time-delay systems, which involve delays in both the state and its derivatives. Our study aims to investigate the stability and observability of transmission lines under both certain and uncertain conditions. To achieve this, we employ the Lyapunov-Krasovskii functional as a key analytical tool. By solving linear matrix inequalities (LMI) and applying optimization theory, we derive new criteria for ensuring stability and observability. These criteria are then validated through simulation results, demon-strating the practical applicability of our theoretical findings. Our approach not only enhances the understanding of transmission line dynamics but also provides robust methodologies for ensuring system reliability and performance.