Systolic Computation Of Multivariable Frequency Response

Peter R Cappello; Alan J Laub

doi:10.1117/12.944046

20 April 1988 Systolic Computation Of Multivariable Frequency Response

Peter R Cappello, Alan J Laub

Proceedings Volume 0880, High Speed Computing; (1988) https://doi.org/10.1117/12.944046
Event: 1988 Los Angeles Symposium: O-E/LASE '88, 1988, Los Angeles, CA, United States

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 .

Citation Download Citation

Peter R Cappello and Alan J Laub "Systolic Computation Of Multivariable Frequency Response", Proc. SPIE 0880, High Speed Computing, (20 April 1988); https://doi.org/10.1117/12.944046

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