Robust adaptive fractional-order observer for a class of fractional-order nonlinear systems with unknown parameters

This paper investigates the parameter and state estimation problems for a class of fractional-order nonlinear systems subject to the perturbation on the observer gain. The fractional-order nonlinear systems are linear in the unknown parameters and nonlinear in the states. Based on the equivalent integer-order differential equations, a fractional-order non-fragile observer and two kinds of fractional-order adaptive law are derived by applying the direct Lyapunov approach. The results are systematically obtained in terms of linear matrix inequalities and solved by YALMIP Matlab Toolbox. Two numerical examples with comparative result of two proposed adaptive laws are provided to illustrate the efficiency and validity of the proposed method.