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• Python Control Systems Library

control.canonical_form — Python Control Systems Library 0.10.2 documentation

control.canonical_form(xsys, form='reachable')[source]

Convert a system into canonical form.

Parameters:

xsysStateSpace object

System to be transformed, with state ‘x’.

formstr

Canonical form for transformation. Chosen from:

• ‘reachable’ - reachable canonical form

• ‘observable’ - observable canonical form

• ‘modal’ - modal canonical form

Returns:

zsysStateSpace object

System in desired canonical form, with state ‘z’.

T(M, M) real ndarray

Coordinate transformation matrix, z = T * x.

Examples

>>> Gs = ct.tf2ss([1], [1, 3, 2])
>>> Gc, T = ct.canonical_form(Gs)  # default reachable
>>> Gc.B
array([[1.],
       [0.]])

>>> Gc, T = ct.canonical_form(Gs, 'observable')
>>> Gc.C
array([[1., 0.]])

>>> Gc, T = ct.canonical_form(Gs, 'modal')
>>> Gc.A                                                    
array([[-2.,  0.],
       [ 0., -1.]])

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