pathsim.utils.gilbert module

pathsim.utils.gilbert.is_numeric(array)

pathsim.utils.gilbert.gilbert_realization(Poles=[], Residues=[], Const=0.0, tolerance=1e-09)

Build real valued statespace model from transfer function in pole residue form by Gilberts method and an additional similarity transformation to get fully real valued matrices.

pole residue form:

H(s) = Const + sum( Residues / (s - Poles) )

statespace form:

H(s) = C * (s*I - A)^-1 * B + D

Notes

The resulting system is identical to the so-called ‘Modal Form’ and is a minimal realization.

Parameters:

• Poles (array) – real and complex poles

• Residues (array) – array of real and complex residue matrices

• Const (array) – matrix for constant term

• tolerance (float) – relative tolerance for checking real poles

Returns:

• A (array) – state matrix

• B (array) – input mapping matrix

• C (array) – state to output projection matrix

• D (array, float) – direct passthrough