equil1

balancing (nonnegative) pair of matrices

Calling Sequence

[T [,siz]]=equil1(P,Q [,tol])

Arguments

: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

Examples

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 balanced realization
• minreal minimal balanced realization
• equil balancing of pair of symmetric matrices
• hankelsv Hankel singular values