Robust H∞ dynamic output feedback control and stability analysis of chaotic nonlinear fractional-order systems with time-varying uncertainties subject to input saturation

This paper introduces a novel [Formula: see text] robust control framework for nonlinear fractional-order systems (FOS) affected by external disturbances, input saturation, and time-varying uncertainties. A dynamic output feedback (DOF) controller is designed to ensure robust asymptotic stability while maintaining high performance under input constraints. The method utilizes Caputo fractional derivatives and advanced time-domain analysis to derive new theorems for stability verification and controller synthesis. By leveraging Linear Matrix Inequalities (LMI), the approach remains computationally efficient while guaranteeing stability and effective disturbance rejection. Key contributions include the characterization of the region of attraction (ROA) and the stable region ([Formula: see text]), extending classical robust control results to fractional-order nonlinear and chaotic systems. Simulation results validate the proposed strategy on chaotic supply chain dynamics, demonstrating enhanced robustness, resilience, and efficiency compared to existing techniques. This study advances the theoretical foundation of nonlinear FOS control and offers a practical, powerful framework for addressing modern control challenges.