A robust decoupling controller for fractional-order multivariable systems with dynamic quantization

This paper proposes an LMI-based framework for robust decoupling control of uncertain fractional-order MIMO systems with input quantization and constant reference tracking. The closed-loop dynamics are decomposed into diagonal and interaction components, and the decoupling problem is formulated using a singular-value-based H∞ criterion. Sufficient LMIs are derived for both maximum and minimum singular values of fractional-order transfer matrices, while the fractional Lyapunov discrepancy induced by the Caputo memory is characterized and bounded in the frequency domain. A reference-aware quantization scheme preserves symmetry around nonzero operating points, and auxiliary dynamics compensate transient saturation mismatch. A history-compatible hybrid zooming strategy certifies admissible zoom-in updates. Under the stated condition of infinitely many certified non-Zeno updates, asymptotic tracking convergence is established. TRMS simulations validate effectiveness.