control.hankel_singular_values

control.hankel_singular_values(sys)[source]

Calculate the Hankel singular values.

Parameters

sysStateSpace: State space system.

Returns

Harray: List of Hankel singular values.

See also

gram

Notes

The Hankel singular values are the singular values of the Hankel operator. In practice, we compute the square root of the eigenvalues of the matrix formed by taking the product of the observability and controllability Gramians. There are other (more efficient) methods based on solving the Lyapunov equation in a particular way (more details soon).

Examples

>>> G = ct.tf2ss([1], [1, 2])
>>> H = ct.hsvd(G)
>>> H[0]
np.float64(0.25)