© 2007

Filtering Theory

With Applications to Fault Detection, Isolation, and Estimation

  • Ali Saberi
  • Anton A. Stoorvogel
  • Peddapullaiah Sannuti

Part of the Systems & Control: Foundations & Applications book series (SCFA)

About this book


The focus of this book is on filtering for linear processes, and its primary goal is to design filters from a class of linear stable unbiased filters that yield an estimation error with the lowest root-mean-square (RMS) norm. Various hierarchical classes of filtering problems are defined based on the availability of statistical knowledge regarding noise, disturbances, and other uncertainties.

An important characteristic of the approach employed in this work for several aspects of filter analysis and design is structural in nature, revealing an inherent freedom to incorporate other classical secondary engineering constraints—such as placement of filter poles at desired locations—in filter design. Such a structural approach requires an understanding of powerful tools that then may be used in several engineering applications besides filtering.

Key features and topics covered:

* Provides an in-depth structural study of powerful tools such as Riccati equations, linear matrix inequalities, and quadratic matrix inequalities.

* Develops a general and structural theory of H2 and H-infinity optimal filtering as well as generalized H2 and H-infinity optimal filtering in a broad framework with an extensive and complete analysis and synthesis of filter design.

* Examines several hierarchically ordered layers of noise decoupled filtering problems under a single umbrella.

* Illustrates the application of filtering theory to fault detection, isolation, and estimation.

Filtering Theory is aimed at a broad audience of practicing engineers, graduate students, and researchers in filtering, signal processing, and control. The book may serve as an advanced graduate text for a course or seminar in filtering theory in applied mathematics or engineering departments. Prerequisites for the reader are a first graduate course in state-space methods as well as a first course in filtering.


Bias Filter H-infinity filtering H2 filtering Information STATISTICA Signal communication networks decoupled filtering delayed filtering filtering theory inverse filtering layers micro-alloy transistor signal processing

Editors and affiliations

  • Ali Saberi
    • 1
  • Anton A. Stoorvogel
    • 2
    • 3
  • Peddapullaiah Sannuti
    • 4
  1. 1.School of Electrical Engineering and Computer ScienceWashington State UniversityPullmanUSA
  2. 2.Department of Mathematics and Computer ScienceEindhoven University of TechnologyMB EindhovenThe Netherlands
  3. 3.Department of Electrical Engineering Mathematics and Computer ScienceDelft University of TechnologyGA DelftThe Netherlands
  4. 4.Department of Electrical and Computer EngineeringRutgers UniversityPiscatawayUSA

Bibliographic information


From the reviews:

The book can be recommended to graduate students and researchers in filtering, signal processing and control. –Zentralblatt Math

"This book is about filtering of white noise and finite energy type signals for finite-dimensional linear time-invariant system models. … This book is written for a mathematically mature reader with background in state space, geometric theory and filtering at least at the first year graduate level in engineering or applied mathematics." (Edwin Engin Yaz, Mathematical Reviews, Issue 2007 j)

"This book presents a comprehensive study of filtering theory from an essentially structural perspective. … this book appears particularly suited to scholars, scientists, and researchers. … the authors also address graduate students and practicing engineers." (Elena Zattoni, International Journal of Robust and Nonlinear Control, Vol. 19, 2009)