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  • Committer: Bazaar Package Importer
  • Author(s): Torsten Werner
  • Date: 2005-01-09 22:58:21 UTC
  • mfrom: (1.1.1 upstream)
  • Revision ID: james.westby@ubuntu.com-20050109225821-473xr8vhgugxxx5j
Tags: 3.0-12
http://bugs.debian.org/255869
changed configure.in to build scilab's own malloc.o, closes: #255869

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man/control/obs_gram.man
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.TH obs_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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obs_gram - observability gramian
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.SH CALLING SEQUENCE
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.nf
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Go=obs_gram(A,C [,dom])
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Go=obs_gram(sl)
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.fi
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.SH PARAMETERS
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.TP 10
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A,C
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: real matrices (of appropriate dimensions)
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.TP 10
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dom
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: string (\fV"d'\fR or \fV"c"\fR (default value))
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.TP 10
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sl
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: \fVsyslin\fR list
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.SH DESCRIPTION
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Observability gramian of the pair \fV(A,C)\fR or linear 
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system \fVsl\fR (\fVsyslin\fR list).
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\fVdom\fR is the domain which can be 
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.TP 
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"c"
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:  continuous system (default)
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.TP
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"d" 
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:  discrete system
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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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                  [  A't    At                      \\   k      k
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             Go = | e  C'C e   dt       or      Go = > A' C'C 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  $$ 
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.LA  Go = \int_0^{\infty} e^{A't}C'Ce^{At}dt 
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.LA  \qquad Go = \sum_{0}^{\infty} {A'}^k C'C{A}^k
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.LA  $$
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.SH EXAMPLE
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.nf
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A=-diag(1:3);C=rand(2,3);
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Go=obs_gram(A,C,'c');     // <=> w=syslin('c',A,[],C); Go=obs_gram(w);
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norm(Go*A+A'*Go+C'*C,1)
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norm(lyap(A,-C'*C,'c')-Go,1)
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A=A/4; Go=obs_gram(A,C,'d');    //discrete time case
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norm(lyap(A,-C'*C,'d')-Go,1)
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.fi
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.SH SEE ALSO
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ctr_gram, obsvss, obsv_mat, lyap