Hassibi, Babak and Kailath, Thomas and Sayed, Ali H. (1999) Array algorithms for H^2 and H^∞ estimation. In: Applied and Computational Control, Signals, and Circuits. Vol.1. Birkhäuser Boston , Boston, MA, pp. 67-120. ISBN 978-1-4612-6822-2. (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20150223-071202056
![]() |
PDF
- Submitted Version
See Usage Policy. 413kB |
Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20150223-071202056
Abstract
Currently, the preferred method for implementing H^2 estimation algorithms is what is called the array form, and includes two main families: square-root array algorithms, that are typically more stable than conventional ones, and fast array algorithms, which, when the system is time-invariant, typically offer an order of magnitude reduction in the computational effort. Using our recent observation that H^∞ filtering coincides with Kalman filtering in Krein space, in this chapter we develop array algorithms for H^∞ filtering. These can be regarded as natural generalizations of their H^2 counterparts, and involve propagating the indefinite square roots of the quantities of interest. The H^∞ square-root and fast array algorithms both have the interesting feature that one does not need to explicitly check for the positivity conditions required for the existence of H^∞ filters. These conditions are built into the algorithms themselves so that an H^∞ estimator of the desired level exists if, and only if, the algorithms can be executed. However, since H^∞ square-root algorithms predominantly use J-unitary transformations, rather than the unitary transformations required in the H^2 case, further investigation is needed to determine the numerical behavior of such algorithms.
Item Type: | Book Section | |||||||||
---|---|---|---|---|---|---|---|---|---|---|
Related URLs: |
| |||||||||
Additional Information: | © 1999 Birkhäuser Boston. This work was supported in part by DARPA through the Department of Air Force under contract F49620-95-1-0525-P00001 and by the Joint Service Electronics Program at Stanford under contract DAAH04-94-G-0058-P-00003. | |||||||||
Funders: |
| |||||||||
DOI: | 10.1007/978-1-4612-0571-5_2 | |||||||||
Record Number: | CaltechAUTHORS:20150223-071202056 | |||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20150223-071202056 | |||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
ID Code: | 55077 | |||||||||
Collection: | CaltechAUTHORS | |||||||||
Deposited By: | Shirley Slattery | |||||||||
Deposited On: | 04 Mar 2015 00:28 | |||||||||
Last Modified: | 10 Nov 2021 20:41 |
Repository Staff Only: item control page