In this monograph, the problem of fault diagnosis in components and actuators of nonlinear systems was considered. A fault diagnosis system at its best must be able to not only detect the presence and isolate the location of faults in a system but also identify them (i.e., estimate their severities) once they are detected and isolated. Hence, a diagnostic system is also equivalently called a fault detection, isolation, and identification (FDII) system. While the importance of fault detection and isolation (FDI) is evident for health monitoring of engineering systems, the importance of fault identification has not been equally recognized in the literature. Consequently, fewer theoretical and practical contributions in the domain of fault identification or severity estimation exist in the literature, especially for nonlinear systems. However, it was shown in Chapter 1 that identification of fault severities is a cornerstone to fault prognosis and subsequently to develop a condition-based maintenance (CBM) system. Furthermore, it was shown that the accurate fault identification is an invaluable asset for fault tolerant control systems, in general, and is a necessity for implementing active fault accommodation and recovery procedures, in particular.