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equil1

balancing (nonnegative) pair of matrices

Syntax

[T, siz] = equil1(P, Q)
[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=blockdiag(S1,S2,zeros(4,4));
Q=blockdiag(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

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