Afif, BenameurSalmi, MohamedBerka, MohammedOzkaya, Umut2025-07-102025-07-1020250948-79211432-0487https://doi.org/10.1007/s00202-025-03173-whttps://hdl.handle.net/20.500.13091/10148This study presents an innovative control approach for enhancing the efficiency and power quality of grid-connected photovoltaic (PV) systems using linear matrix inequality (LMI) techniques. The primary objective is to develop a robust maximum power point tracking (MPPT) controller that ensures maximum energy extraction under varying solar irradiation conditions while improving the stability and reliability of power transfer to the grid. The system architecture comprises PV panels connected to a boost converter, managed by the LMI-based MPPT and a three-phase bidirectional converter that enables bidirectional power flow between the grid and the load. This work contrasts the performance of the proposed LMI method with the traditional sliding mode control (SMC), addressing the limitations of SMC, such as the chattering phenomenon and reduced efficiency under dynamic conditions. Key objectives include achieving superior power tracking accuracy, minimizing total harmonic distortion (THD) in the grid current, and ensuring smooth voltage regulation. Simulations demonstrate that the LMI-based MPPT controller delivers 2-3% higher power output compared to SMC across various solar irradiation scenarios, including rapid fluctuations and partial shading. The LMI methodology also significantly reduces THD by 20-30%, enhancing the power quality and ensuring compliance with grid standards. Additionally, the LMI control strategy eliminates the chattering effect observed in SMC, resulting in smoother control dynamics and improved system stability. These findings underscore the potential of the LMI approach to optimize energy harvesting, improve grid compatibility, and provide a reliable solution for modern PV systems, contributing to the advancement of sustainable energy technologies.eninfo:eu-repo/semantics/closedAccessLinear Matrix InequalityMaximum Power Point TrackingSliding ModeTotal Harmonic DistortionArticle10.1007/s00202-025-03173-w2-s2.0-105007155799