Stabilization using the separation principle for generalized classes of fractional-order fuzzy systems

The separation principle has been extensively used in the literature to tackle the observer-based control problem for integer-order linear and Lipschitz nonlinear systems. However, less interest has been given by researchers to treat the same problem, in the fractional-order framework. In this context, this paper introduces and investigates a separation principle tailored for two advantageous classes of nonlinear fractional-order fuzzy systems. These two classes can be regarded as generalizations of the classical nonlinear Lipshchitz systems. The research explores both asymptotic stability and practical Mittag-Leffler stability, unveiling a novel approach to handling intricate fractional-order systems with fuzzy characteristics. Through rigorous theoretical analysis and simulation studies, the paper demonstrates the efficacy and applicability of the separation principle, for both considered classes of fractional fuzzy systems.