The objective of this book is to present the up-to-date research developments and novel methodologies on state estimation and fault diagnosis (FD) techniques for a class of complex systems subject to closed-loop control, nonlinearities, and stochastic phenomena. It covers state estimation design methodologies and FD unit design methodologies including framework of optimal filter and FD unit design, robust filter and FD unit design, stability, and performance analysis for the considered systems subject to various kinds of complex factors.Features: Reviews latest research results on the state estimation and fault diagnosis issues. Presents comprehensive framework constituted for systems under imperfect measurements. Includes quantitative performance analyses to solve problems in practical situations. Provides simulation examples extracted from practical engineering scenarios. Discusses proper and novel techniques such as the Carleman approximation and completing the square method is employed to solve the mathematical problems. This book aims at Graduate students, Professionals and Researchers in Control Science and Application, Stochastic Process, Fault Diagnosis, and Instrumentation and Measurement.