Disturbance observer-based delayed robust feedback control design for a class of uncertain variable fractional-order systems: Order-dependent and delay-dependent stability.

This work addresses the stabilization of variable fractional-order (VFO) neutral-type systems with structure perturbations and unknown disturbance signals using the feedback control approach. The goal is to design disturbance-observer-based delayed state- and output-feedback controllers to achieve robust stability of such VFO systems. The proposed controller consists of two parts, namely a primary controller based on the linear feedback technique, and an auxiliary controller based on the disturbance observer. A disturbance observer is developed to estimate the disturbance signal, which is generated by an exogenous system. Based on matrix inequalities, order-dependent and delay-dependent conditions are formulated via FO Lyapunov theory that guarantee the robust stability of the closed-loop system. Simulations verify the main results.