Fractional-Order Adaptive Fault Estimation for a Class of Nonlinear Fractional-Order Systems

This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order alpha belongs to 0 < alpha < 1. A numerical example is given to demonstrate the validity of the proposed approach.