Reduced-Order State Estimation for a Class of Nonlinear Fractional-Order Systems

This paper studies the state estimation problem for a class of nonlinear fractional-order systems subject to external disturbances. The nonlinear function in the plans is assumed to be satisfied the one-sided Lipschitz condition and the quadratically inner-bounded condition. We first propose a new reduced-order fractional-order observer for the nonlinear fractional-order systems. Then, based on some results on the Caputo fractional derivative combined with Cauchy matrix inequality and Schur complement lemma, we establish a new sufficient condition to ensure the stability of the error dynamic. Three examples are provided to demonstrate the effectiveness of the proposed method.