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ctr_gram(1) Scilab Function ctr_gram(1)
NAME
ctr_gram - controllability gramian
CALLING SEQUENCE
[Gc]=ctr_gram(A,B [,dom])
[Gc]=ctr_gram(sl)
PARAMETERS
A,B : two real matrices of appropriate dimensions
dom : character string ('c' (default value) or 'd')
sl : linear system, syslin list
DESCRIPTION
Controllability gramian of (A,B) or sl (a syslin linear system).
dom character string giving the time domain : "d" for a discrete time sys-
tem and "c" for continuous time (default case).
/+inf ---+inf
[ At ' A't \ k k
Gc = | e BB e dt Gc = > A BB' A'
] /
/0 ---0
EXAMPLE
A=diag([-1,-2,-3]);B=rand(3,2);
Wc=ctr_gram(A,B)
U=rand(3,3);A1=U*A/U;B1=U*B;
Wc1=ctr_gram(A1,B1) //Not invariant!
SEE ALSO
equil1, obs_gram, contr, cont_mat, cont_frm, contrss
AUTHOR
S. Steer INRIA 1988
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