Tbis book is basicaUy concemed with approaches for improving safety in man-made systems. We caU these approaches, coUectively, fault monitoring, since they are concemed primarily with detecting faults occurring in the components of such systems, being sensors, actuators, controUed plants or entire strucutures. The common feature of these approaches is the intention to detect an abrupt change in some characteristic property of the considered object, by monitoring the behavior of the system. This change may be a slow-evolving effect or a complete breakdoWD. In tbis sense, fault monitoring touches upon, and occasionaUy overIaps with, other areas of control engineering such as adaptive control, robust controller design, reIiabiIity and safety engineering, ergonomics and man-macbine interfacing, etc. In fact, a system safety problem, could be attacked from any of the above angles of view. In tbis book, we don't touch upon these areas, unless there is a strong relationship between the fauIt monitoring approaches discussed and the aforementioned fields. When we set out to write tbis book, our aim was to incIude as much material as possible in a most rigorous, unified and concise format. Tbis would incIude state-of-the-art method as weil as more cIassical techniques, stilI in use today. AB we proceeded in gathering material, however, it soon became apparent that these were contradicting design criteria and a trade-off had to be made. We believe that the completeness vs.