nengolib.signal.balanced_transformation

nengolib.signal.balanced_transformation(sys)

Computes the balancing transformation, its inverse, and eigenvalues.

Parameters:

sys : linear_system_like

Linear system representation.

Returns:

T : (len(sys), len(sys)) np.array

Similarity transformation matrix.

Tinv : (len(sys), len(sys)) np.array

Inverse of similarity transformation matrix.

s : (len(sys),) np.array

Hankel singular values (see hsvd()).

See also

balance(), Balanced, hsvd(), LinearSystem.transform()

References

[1]	Laub, A.J., M.T. Heath, C.C. Paige, and R.C. Ward, “Computation of System Balancing Transformations and Other Applications of Simultaneous Diagonalization Algorithms,” IEEE Trans. Automatic Control, AC-32 (1987), pp. 115-122.

[2]	http://www.mathworks.com/help/control/ref/balreal.html