Robust H_∞-control of chaotic fractional-order systems: dynamic output feedback with saturation and external disturbance resilience

Nonlinear fractional-order systems (FOS) with chaotic dynamics face significant stability challenges under input saturation and external disturbances. This paper proposes a robust textbackslashtextHtextbackslashinfty dynamic output feedback (DOF) controller to stabilize FOS with fractional orders 0 textless textbackslashalpha textless 1. Leveraging the Gronwall-Bellman lemma and Linear Matrix Inequalities (LMIs), the proposed approach ensures oscillation-free convergence, minimizes control effort prior to saturation, and provides a stable region (textbackslashtextBtextbackslashupepsilon ) along with a computable region of attraction (ROA). Additionally, a novel Saturation Resilience Index (SRI) is introduced to quantify performance under saturation, achieving SRI value of 0.156. Simulation results demonstrate effective disturbance rejection and validate the practical applicability of the framework for controlling chaotic systems under realistic constraints. These findings position the proposed strategy as a robust and efficient solution for nonlinear fractional-order systems.