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.TH obs_gram 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
obs_gram - observability gramian
.SH CALLING SEQUENCE
.nf
Go=obs_gram(A,C [,dom])
Go=obs_gram(sl)
.fi
.SH PARAMETERS
.TP 10
A,C
: real matrices (of appropriate dimensions)
.TP 10
dom
: string (\fV"d'\fR or \fV"c"\fR (default value))
.TP 10
sl
: \fVsyslin\fR list
.SH DESCRIPTION
Observability gramian of the pair \fV(A,C)\fR or linear
system \fVsl\fR (\fVsyslin\fR list).
\fVdom\fR is the domain which can be
.TP
"c"
: continuous system (default)
.TP
"d"
: discrete system
.LP
.IG
.nf
/+inf ---+inf
[ A't At \\ k k
Go = | e C'C e dt or Go = > A' C'C A
] /
/0 ---0
.fi
.FI
.LA $$
.LA Go = \int_0^{\infty} e^{A't}C'Ce^{At}dt
.LA \qquad Go = \sum_{0}^{\infty} {A'}^k C'C{A}^k
.LA $$
.SH EXAMPLE
.nf
A=-diag(1:3);C=rand(2,3);
Go=obs_gram(A,C,'c'); // <=> w=syslin('c',A,[],C); Go=obs_gram(w);
norm(Go*A+A'*Go+C'*C,1)
norm(lyap(A,-C'*C,'c')-Go,1)
A=A/4; Go=obs_gram(A,C,'d'); //discrete time case
norm(lyap(A,-C'*C,'d')-Go,1)
.fi
.SH SEE ALSO
ctr_gram, obsvss, obsv_mat, lyap
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