Observer-based practical stabilization of fractional-order systems via linear matrix inequalities

Abstract

This paper investigates the problem of observer-based stabilization for a class of nonlinear fractional-order systems affected by bounded disturbances. The considered nonlinearities satisfy the quasi-one-sided Lipschitz condition, which generalizes the classical one-sided Lipschitz property and allows treating a broader class of nonlinear dynamics that are not necessarily Lipschitz continuous. First, sufficient conditions ensuring the global uniform practical Mittag-Leffler stability of both the observer error dynamics and the state-feedback closed-loop system are derived in terms of Linear Matrix Inequalities (LMIs). Then, an observer-based output feedback controller is designed by combining the state-feedback law and the fractional-order observer. The proposed separation principle guarantees the practical Mittag-Leffler stability of the overall closed-loop system. An illustrative numerical example is provided to demonstrate the effectiveness and reduced conservatism of the proposed design.