control.gram

control.gram(sys, type)[source]

Gramian (controllability or observability).

Parameters

sysStateSpace: System description.
typeString: 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

gram2D array: Gramian of system.

Raises

ValueError

If system is not instance of StateSpace class, or
if type is not ‘c’, ‘o’, ‘cf’ or ‘of’, or
if system is unstable (sys.A has eigenvalues not in left half plane).

ControlSlycot

If slycot routine sb03md cannot be found or if slycot routine sb03od cannot be found.

Examples

>>> G = ct.rss(4)
>>> Wc = ct.gram(G, 'c')
>>> Wo = ct.gram(G, 'o')
>>> Rc = ct.gram(G, 'cf')  # where Wc = Rc' * Rc
>>> Ro = ct.gram(G, 'of')  # where Wo = Ro' * Ro