Robust Stability Analysis of Grid-Following Inverters: Integrating Parametric Uncertainty and Interval Time Delay for PI Controller Tuning

This paper presents a novel robust stability analysis framework for grid-following inverters subject to interval parametric uncertainties and unknown but bounded time delays. Prior works employing classical robust control strategies, such as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control, μ-synthesis, and sliding mode control, often result in high-order or nonlinear controllers that are difficult to tune and implement in real-time inverter applications. Moreover, they typically address either parametric uncertainties or constant delays, but not their combined and varying effects. Model-free control approaches, including reinforcement learning and data-driven methods, offer adaptability but require extensive training data and computational effort, and often lack formal stability guarantees. In contrast to conventional delay-aware methods—such as Bode plot-based techniques, Lyapunov-Krasovskii functionals, and Smith Predictors—that either assume fixed parameter values or exhibit conservatism under uncertainty, the proposed approach employs a delay-dependent criterion integrated with value set and zero exclusion principles. The proposed method is simple, systematic, and non-conservative, enabling the complete determination of PI stabilizing gains without complex tuning. Simulation and experimental results verify its practical robustness and suitability for real-world inverter control.