control.similarity_transform

control.similarity_transform(xsys, T, timescale=1, inverse=False)[source]

Perform a similarity transformation, with option time rescaling.

Transform a linear state space system to a new state space representation z = T x, or x = T z, where T is an invertible matrix.

Parameters

xsys (StateSpace object) – System to transform
T ((M, M) array_like) – The matrix T defines the new set of coordinates z = T x.
timescale (float, optional) – If present, also rescale the time unit to tau = timescale * t
inverse (bool, optional) – If True (default), transform so z = T x. If False, transform so x = T z.

Returns

zsys – System in transformed coordinates, with state ‘z’

Return type

StateSpace object

Examples

>>> Gs = ct.tf2ss([1], [1, 3, 2])
>>> Gs.A
array([[-3., -2.],
       [ 1.,  0.]])

>>> T = np.array([[0, 1], [1, 0]])
>>> Gt = ct.similarity_transform(Gs, T)
>>> Gt.A
array([[ 0.,  1.],
       [-2., -3.]])