There is an increasing demand for man-made dynamic systems to operate autonomously in the presence of faults and failures in sensors, actuators, or components. Fault detection and identification are essential components of an autonomous system. Hence, a high demand exists for the development of intelligent systems that are able to autonomously detect the presence and isolate the location of faults occurring in different components of complex dynamic systems. Especially faults in a control loop are of particular importance as they may instantly result in instability of the controlled system. Thus, it is crucial that faults are efficiently and timely detected and isolated while the system is in operation. This is essentially the concept of online health monitoring though, in general, health monitoring may also be performed offline using stored data in a post-processing capacity to determine if the system overhaul is necessary. In general, autonomous online health monitoring and fault diagnosis is essential for mission- and safety-critical systems as opposed to fail-operational systems, where offline health monitoring and fault diagnosis is usually sufficient – in order to perform maintenance. In this monograph, the main focus is on developing a fault diagnosis (FD) methodology that enables online health monitoring of nonlinear systems; however, the proposed approach can as well be applied for offline monitoring purposes.