Fault detection and reconstruction via both full-order and reduced-order sliding mode observers for uncertain nonlinear systems

This paper considers the problems of fault detection and reconstruction for uncertain nonlinear Lipschitz systems when the so-called structural matching condition is satisfied. The admissible Lipschitz constant of the system is maximized through linear matrix inequality (LMI) optimization. This significantly extends previous results by considering a more general class of system nonlinearities. A full-order sliding mode observer is considered to asymptotically estimate the system states in a finite time when no actuator fault occurs. Based on the observer, we produce a residual which can be used to detect the occurrence of the actuator fault when at least one actuator fault occurs indeed. After this, a reduced-order sliding mode observer is constructed by choosing a special observer gain matrix. The reduced order observer is able to reconstruct the actuator faults using the equivalent output injection concept. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods.