Péter Gáspár, Zoltán Szabó, József Bokor

Discrete Feedback Systems 1.

Classical Control

A.1.2 Singular value decomposition

Theorem A.1 (SVD) Suppose

is an

matrix whose entries come from the field

, which is either the field of real numbers or the field of complex numbers. Then there exists a factorization of the form

where

is an

unitary matrix over

, the matrix

diagonal matrix with nonnegative real numbers on the diagonal, and

is an

unitary matrix over

. Such a factorization is called a singular-value decomposition of

. A common convention is to order the diagonal entries

in non-increasing fashion. In this case, the diagonal matrix

is uniquely determined by

(though the matrices

and

are not). The diagonal entries of

are known as the singular values of

. More precisely

has the form

where

and

Remark A.1 (Pseudo-inverse) The singular value decomposition can be used for computing the pseudo-inverse of a matrix. Indeed, the pseudo-inverse of the matrix

with singular value decomposition

where

is the pseudo-inverse of

with every nonzero entry replaced by its reciprocal.

Tartalomjegyzék

Kiadó: Akadémiai Kiadó

Online megjelenés éve: 2019

ISBN: 978 963 454 372 5

The aim of the book is to provide a well-rounded exposure to analysis, control and simulation of discrete-time systems. Theoretical techniques for studying discrete-time linear systems with particular emphasis on the properties and design of sampled data feedback control systems are introduced. This book is intended to be used as a textbook in our MSc and PhD courses. We have tried to balance the broadness and the depth of the material covered in the book. The interested reader is also sent to consult the publications of the references list.

Hivatkozás: https://mersz.hu/gaspar-szabo-bokor-discrete-feedback-systems-1//

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