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equil1(1) Scilab Function equil1(1)
NAME
equil1 - balancing (nonnegative) pair of matrices
CALLING SEQUENCE
[T [,siz]]=equil1(P,Q [,tol])
PARAMETERS
P, Q : two non-negative symmetric matrices
T : nonsingular matrix
siz : vector of three integers
tol : threshold
DESCRIPTION
equil1 computes t such that:
P1=T*P*T' and Q1=inv(T)'*Q*inv(T) are as follows:
P1 = diag(S1,S2,0,0) and Q1 = diag(S1,0,S3,0) with S1,S2,S3 positive and
diagonal matrices with respective dimensions siz=[n1,n2,n3]
tol is a threshold for rank determination in SVD
EXAMPLE
S1=rand(2,2);S1=S1*S1';
S2=rand(2,2);S2=S2*S2';
S3=rand(2,2);S3=S3*S3';
P=sysdiag(S1,S2,zeros(4,4));
Q=sysdiag(S1,zeros(2,2),S3,zeros(2,2));
X=rand(8,8);
P=X*P*X';Q=inv(X)'*Q*inv(X);
[T,siz]=equil1(P,Q);
P1=clean(T*P*T')
Q1=clean(inv(T)'*Q*inv(T))
SEE ALSO
balreal, minreal, equil, hankelsv
AUTHOR
S. Steer 1987
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