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Proceedings Paper

Systolic Computation Of Multivariable Frequency Response
Author(s): Peter R Cappello; Alan J Laub
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Paper Abstract

A systolic organization is presented for the computation of a complex-valued frequency response matrix G (j 0)) = C (j w- A)-1B . By 'sys-tolic organization,' we mean an algorithm intended for software implementation on a programmable systolic/wavefront computer system. Typically, the real-valued state space model matrices A , B , and C are given and the calculation of G must be performed for a very large number of values of the scalar "frequency" parameter co. This, and closely related calculations, arise naturally in the analysis and design of control systems. The algorithm which has been chosen for systolic implementation is an orthogonal version of an algorithm appearing pre-viously in the literature. The matrix A is reduced initially to an upper Hessenberg form and this form is preserved as w varies subsequently in the matrix j wl - A . A systolic QR factorization of this latter matrix [(jl - A) = QT R} is then implemented for effecting the linear system solution (inversion). The critical computational component is CR-1. This computational component's process dependency graph is embedded optimally in space and time through the use of a nonlinear spacetime transformation. The computational period of the algorithm is 0 (n) where n is the order of the matrix A .

Paper Details

Date Published: 20 April 1988
PDF: 8 pages
Proc. SPIE 0880, High Speed Computing, (20 April 1988); doi: 10.1117/12.944046
Show Author Affiliations
Peter R Cappello, University of California (United States)
Alan J Laub, University of California (United States)

Published in SPIE Proceedings Vol. 0880:
High Speed Computing
David P. Casasent, Editor(s)

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