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  • Committer: Bazaar Package Importer
  • Author(s): Torsten Werner
  • Date: 2002-03-21 16:57:43 UTC
  • Revision ID: james.westby@ubuntu.com-20020321165743-e9mv12c1tb1plztg
Tags: upstream-2.6
Import upstream version 2.6

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man/control/ctr_gram.man
 
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.TH ctr_gram 1 "April 1993" "Scilab Group" "Scilab Function"
 
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.so ../sci.an 
 
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.SH NAME
 
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ctr_gram - controllability gramian
 
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.SH CALLING SEQUENCE
 
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.nf
 
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[Gc]=ctr_gram(A,B [,dom])
 
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[Gc]=ctr_gram(sl)
 
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.fi
 
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.SH PARAMETERS
 
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.TP 10
 
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A,B
 
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: two real matrices of appropriate dimensions
 
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.TP
 
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dom
 
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: character string (\fV'c'\fR (default value) or \fV'd'\fR)
 
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.TP
 
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sl
 
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: linear system, \fVsyslin\fR list
 
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.SH DESCRIPTION
 
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Controllability gramian of \fV(A,B)\fR or \fVsl\fR (a \fVsyslin\fR 
 
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linear system).
 
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.LP
 
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\fVdom\fR character string giving the time domain : \fV"d"\fR for a
 
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discrete time system and \fV"c"\fR for continuous time (default case).
 
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.LP
 
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.IG 
 
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.nf
 
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                  /+inf                             ---+inf
 
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                  [  At  ' A't                      \\   k      k
 
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             Gc = | e  BB e   dt               Gc =  > A BB' A'
 
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                  ]                                 /
 
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                 /0                                 ---0
 
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.fi
 
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.FI
 
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.LA  $$ 
 
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.LA  Gc = \int_0^{\infty} e^{At}BB'e^{A't}dt 
 
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.LA  \qquad Gc = \sum_{0}^{\infty} A^k B B'{A'}^k
 
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.LA  $$
 
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.SH EXAMPLE
 
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.nf
 
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A=diag([-1,-2,-3]);B=rand(3,2);
 
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Wc=ctr_gram(A,B)
 
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U=rand(3,3);A1=U*A/U;B1=U*B;
 
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Wc1=ctr_gram(A1,B1)    //Not invariant!
 
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.fi
 
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.SH SEE ALSO
 
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equil1, obs_gram, contr, cont_mat, cont_frm, contrss
 
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.SH AUTHOR
 
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S. Steer INRIA 1988