Observer Design for Fractional-Order Polynomial Fuzzy Systems Depending on a Parameter

For fractional-order systems, observer design is remarkable for the estimation of unavailable states from measurable outputs. In addition, the nonlinear dynamics and the presence of parameters that can vary over different operating conditions or time, such as load or temperature, increase the complexity of the observer design. In view of the aforementioned factors, this paper investigates the observer design problem for a class of Fractional-Order Polynomial Fuzzy Systems (FORPSs) depending on a parameter. The Caputo-Hadamard derivative is considered in this study. First, we prove the practical Mittag-Leffler stability, using the Lyapunov methods, for the general case of Caputo-Hadamard Fractional-Order Systems (CHFOSs) depending on a parameter. Secondly, based on this stability theory, we design an observer for the considered class of FORPSs. The state estimation error is ensured to be practically generalized Mittag-Leffler stable by solving Sum Of Squares (SOSs) conditions using the developed SOSTOOLS.