Adaptive Stabilization for a Class of Fractional-Order Systems with Nonlinear Uncertainty

The stabilization task for uncertain integer-order systems has been widely and extensively investigated in the literature. However, stabilizing uncertain fractional-order systems (despite the recent great interest given by researchers to this research axis) is still considered as a fertile area of research. In this paper, an original adaptive scheme to handle this particular problem, under the nonlinear uncertainty modeling, is suggested. The approach consists of estimating the upper bound of uncertainties and designing an adaptive output feedback controller, using the Lyapunov direct method. The concept of uniform practical Mittag-Leffler stability is used throughout the paper. The feasibility and effectiveness of the theoretical results are shown through simulations via two numerical examples.