Fault Estimation Based Control Design for Nonlinear Fractional‐Order Systems Under Proportional‐Integral Observer

This study addresses the issue of finite‐time observer‐based control design for a nonlinear fractional‐order system under additive faults and disturbances. The main motive is to construct a nonlinear fractional‐order proportional‐integral observer such that it simultaneously estimates the states and fault signal. A controller is designed to overcome the mismatch between the quantization parameters, and also the estimated fault signal is incorporated in the control design to eliminate the effects of the fault in the system. Furthermore, by choosing an appropriate Lyapunov function, the results are deduced in terms of linear matrix inequalities, based on which the observer and controller gain values are obtained. Then the viability of the developed controller and observer is verified by numerical simulation results.