control.matlab.gram

control.matlab.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