make_continuous_time_companion_matrix
- hcipy.util.make_continuous_time_companion_matrix(poles, rtol=1e-09)[source]
Create a continuous-time companion matrix from poles.
For a system with poles p1, p2, …, pn, creates the controllable companion form state matrix that has these poles as eigenvalues.
- Parameters:
- polesarray_like
Poles (eigenvalues) of the system. For stable systems, poles should have negative real parts.
- rtolfloat, optional
The relative tolerance which which the poles are required to be complex conjugate pairs. Default: 1e-9.
- Returns:
- transition_matrixndarray
Companion form state matrix (n x n).
- observation_matrixndarray
Observation matrix (1 x n), selects the first state.
- Raises:
- ValueError
When the poles are not real or do not form complex conjugate pairs.