B. Hassibi, A. H. Sayed, and T. Kailath, *Indefinite Quadratic Estimation and Control, * SIAM, PA, 1999.

**Description**: This monograph presents a unified mathematical framework for a wide range of problems in estimation and control. The authors discuss the two most commonly used methodologies: the stochastic H^{2} approach and the deterministic (worst-case) H approach. Despite the fundamental differences in the philosophies of these two approaches, the authors have discovered that, if indefinite metric spaces are considered, they can be treated in the same way and are essentially the same. The benefits and consequences of this unification are pursued in detail, with discussions of how to generalize well-known results from H^{2} theory to H setting, as well as new results and insight, the development of new algorithms, and applications to adaptive signal processing.

The authors deliberately have placed primary emphasis on estimation problems which enable one to solve all the relevant control problems in detail. They also deal mostly with discrete-time systems, since these are the ones most important in current applications.

#### Audience

Written for the second-year graduate student in electrical, mechanical, or aerospace engineering, the book requires a basic understanding of linear algebra and linear systems theory. Researchers in systems and control, signal processing, communications, and numerical algorithm development will also find this book useful.

#### Contents

Preface; Chapter 1: Introduction and Motivation; Chapter 2: Linear Estimation in Krein Spaces; Chapter 3: State-Space Models in Krein Space; Chapter 4: Finite-Horizon HFiltering; Chapter 5: Array Algorithms; Chapter 6: Several Related Problems; Chapter 7: H Optimality of the LMS Algorithm; Chapter 8: Duality; Chapter 9: Finite-Horizon Control Problems; Chapter 10: Input-Output Approach to H^{2} and H Estimation; Chapter 11: Input-Output Approach to H^{2} and H Control; Chapter 12: The Discrete-Time Algebraic Riccati Equation; Chapter 13: Infinite-Horizon Results for State-Space Models; Chapter 14: Asymptotic Behavior; Chapter 15: Optimal H Solutions; Chapter 16: Continuous-Time Results and Final Remarks; Bibliography; Index.

#### About the Authors

Babak Hassibi is a member of the technical staff at Bell Labs in Murray Hill, New Jersey. Ali H. Sayed is an Associate Professor in the Department of Electrical Engineering at the University of California, Los Angeles. Thomas Kailath is Hitachi America Professor of Engineering at Stanford University in California.

1999 / xvii + 555 pages / Hardcover / ISBN 0-89871-411-7

List Price $80.00 / SIAM Member Price $64.00 / **Order Code AM16**