Practical Separation Principle of Quasi‐One‐Sided Caputo Fractional‐Order Systems

ABSTRACT In this study, the global practical Mittag–Leffler stabilization of a class of nonlinear fractional‐order systems satisfying a (weak) one‐sided Lipschitz condition is investigated. For the considered one‐sided Lipschitz nonlinear systems, a sufficient condition ensuring the existence of a state observer is first established. Then, an observer‐based state feedback controller is proposed, and conditions guaranteeing the practical stability of the resulting closed‐loop fractional‐order system are derived via a linear matrix inequality approach. The separation principle is obtained for the observer‐based control design. The main results extend and improve existing results in the literature. A numerical example is provided to illustrate the effectiveness and applicability of the proposed approach.