hankelsv

Hankel singular values

Calling Sequence

[nk2,W]=hankelsv(sl [,tol])
[nk2]=hankelsv(sl [,tol])

Arguments

:sl syslin list representing the linear system (state-space). : :tol tolerance parameter for detecting imaginary axis modes (default

value is 1000*%eps).

:

Description

returns nk2, the squared Hankel singular values of sl and W = P*Q = controllability gramian times observability gramian.

nk2 is the vector of eigenvalues of W.

Examples

A=`diag`_([-1,-2,-3]);
sl=`syslin`_('c',A,`rand`_(3,2),`rand`_(2,3));[nk2,W]=hankelsv(sl)
[Q,M]=`pbig`_(W,nk2(2)-%eps,'c');
slr=`projsl`_(sl,Q,M);hankelsv(slr)

See Also

• balreal balanced realization
• equil balancing of pair of symmetric matrices
• equil1 balancing (nonnegative) pair of matrices