INDEFINITE QUADRATIC ESTIMATION AND CONTROL:
A Unified Approach to H_2 and H_oo Theories

B. Hassibi, A. H. Sayed, and T. Kailath

Studies in Applied Mathematics, vol. 16,
SIAM, PA. Hardcover. xvii+555 pages.
ISBN 0-89871-411-7.


Descirption:

This monograph presents a unified mathematical framework
for a wide range of problems in estimation and control.
The authors discuss two most commonly used methodologies:
the stochastic H_2 approach and the deterministic (worst-
case) H_oo 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 the H_oo setting, as well as new results and insights,
the development of new algorithms, and applications to
adaptive signal processing.

Table of Contents:

 1. Introduction and Motivation
 2. Linear Estimation in Krein Spaces
 3. State-Space Models in Krein Space
 4. Finite Horizon H_oo Filtering
 5. Array Algorithms
 6. Several Related Problems
 7. H_oo Optimality of the LMS Algorithm
 8. Duality
 9. Finite-Horizon Control Problems
10. Input-Output Approach to H_2 and H_oo Estimation
11. Input-Output Approach to H_2 and H_oo Control
12. The Discrete-Time Algebraic Riccati Equation
13. Infinite-Horizon Results for State-Space Models
14. Asymptotic Behavior
15. Optimal H_oo Solutions
16. Continuous-Time Results and Final Remarks

Bibliography
Index


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.


About the Authors:

B. Hassibi is with Bell Laboratories, Murray Hill, NJ.
A. H. Sayed is Associate Prof. of Electrical Eng., UCLA
T. Kailath is Hitachi America Prof. of Eng., Stanford Univ.