Ali Saberi & Anton A. Stoorvogel 
Filtering Theory 
With Applications to Fault Detection, Isolation, and Estimation

As soon as we (AS and PS) completed writing the book on H Optimal Con- 2 trol, another task of equal magnitude was laid to our charge. This task was to work on ?ltering and related topics. This book releases us from this charge. In this endeavor, we are fortunate to have found a capable person in our friend and colleague (AAS) who helped us release our burden. The subject of ?ltering is indeed vast and immense, much more so than the subject of H Optimal Control. In this work, we have tried to present what we 2 believe to be the fundamental issues of ?ltering. The book is not intended to give a chronological development of ?ltering from a historical point of view. A vast number of books already do so. Our intent here is to develop from our perspective the complete theory of ?ltering and various design methodologies associated with it along with their practical implementations. In this respect, we present here a state-of-the-art view of exact and almost input-decoupled ?ltering, H , and H 2 1 ?ltering and inverse ?ltering issues, and include an application of ?ltering and inverse ?ltering to fault detection, isolation, and estimation. Most of the work reported here arose out of the research conducted by one or more of us and so- times in collaboration with our students and colleagues. Supposedly, young F.

Table of Content

Preliminaries.- A special coordinate basis (SCB) of linear multivariable systems.- Algebraic Riccati equations and matrix inequalities.- Exact disturbance decoupling via state and full information feedback.- Almost disturbance decoupling via state and full information feedback.- Exact input-decoupling filters.- Almost input-decoupled filtering under white noise input.- Almost input-decoupled filtering without statistical assumptions on input.- Optimally (suboptimally) input-decoupling filtering under white noise input—H2 filtering.- Optimally (suboptimally) input-decoupled filtering without statistical information on the input-H? filtering.- Generalized H2 suboptimally input-decoupled filtering.- Generalized H? suboptimally input-decoupled filtering.- Fault detection, isolation, and estimation—exact or almost fault estimation.- Fault detection, isolation, and estimation—optimal fault estimation.