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Aide de Scilab >> CACSD (Computer Aided Control Systems Design) > equil1

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
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Last updated:
Thu Oct 02 13:54:31 CEST 2014