Difference between revisions of "Errata: Explanation of the lack of zeros when B or C is full rank is confusing"

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{{errata page
 
{{errata page
| chapter = <!-- Replace with the (capitalized) chapter name where the error occurs -->
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| chapter = Transfer Functions
| page = <!-- Page number of the erratum -->
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| page = 240
| line = <!-- Line number of the erratum -->
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| line = -11
| contributor = <!-- Name of the contributor. Uses initials + last name (R. M. Murray) -->
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| contributor = S. Fuller
| date = <!-- Date on which the erratum was reported -->
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| date = 29 April 2008
| version = <!-- Version in which the erratum occurred (usually 'First printing') -->
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| version = First printing
| text = <!-- Text for the description of the error and the fix.  This can be multiple lines, but can't include templates -->
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| text =
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In the paragraph following equation (8.17), the text states that there are no zeros if either the <math>B</math> or <math>C</math> matrix is "full rank".  This wording is misleading since a non-square matrix can be full rank without having fully independent rows (for <math>B</math>) or columns (for <math>C</math>).  The text should read
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<blockquote>
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Notice in particular that if the matrix <math>B</math> has full <font color=blue>row</font> rank, then the matrix
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in equation (8.17) has <math>n</math> linearly independent rows for all values of <math>s</math>.  Similarly there are <math>n</math> linearly independent columns if the matrix <math>C</math> has full <font color=blue>column</font> rank. This implies that systems where the matrix <math>B</math> or <math>C</math> is <font color=blue>square and</font> full rank do not have zeros. In particular it means that a system has no zeros if it is fully actuated\index{fully actuated systems} (each state can be controlled independently) or if the full state is measured.
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</blockquote>
 
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Revision as of 17:13, 17 May 2008


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Location: page 240, line -11

In the paragraph following equation (8.17), the text states that there are no zeros if either the or matrix is "full rank". This wording is misleading since a non-square matrix can be full rank without having fully independent rows (for ) or columns (for ). The text should read

Notice in particular that if the matrix has full row rank, then the matrix in equation (8.17) has linearly independent rows for all values of . Similarly there are linearly independent columns if the matrix has full column rank. This implies that systems where the matrix or is square and full rank do not have zeros. In particular it means that a system has no zeros if it is fully actuated\index{fully actuated systems} (each state can be controlled independently) or if the full state is measured.

(Contributed by S. Fuller, 29 April 2008)