control.gram¶
-
control.
gram
(sys, type)¶ Gramian (controllability or observability)
- Parameters
sys (StateSpace) – System description
type (String) – Type of desired computation. type is either ‘c’ (controllability) or ‘o’ (observability). To compute the Cholesky factors of Gramians use ‘cf’ (controllability) or ‘of’ (observability)
- Returns
gram – Gramian of system
- Return type
2D array (or matrix)
- Raises
ValueError –
if system is not instance of StateSpace class * if type is not ‘c’, ‘o’, ‘cf’ or ‘of’ * if system is unstable (sys.A has eigenvalues not in left half plane)
ImportError – if slycot routine sb03md cannot be found if slycot routine sb03od cannot be found
Notes
The return type for 2D arrays depends on the default class set for state space operations. See
use_numpy_matrix()
.Examples
>>> Wc = gram(sys, 'c') >>> Wo = gram(sys, 'o') >>> Rc = gram(sys, 'cf'), where Wc = Rc' * Rc >>> Ro = gram(sys, 'of'), where Wo = Ro' * Ro