def spectral_radius(model):
if not isinstance(model, sys.dlti):
model = sys.dlti(*model)
poles = model.poles
if poles.size == 0:
return None
return np.max(np.absolute(poles))
def output_range(model, input_range):
if not isinstance(model, sys.dlti):
model = sys.dlti(*model)
if not isinstance(input_range, Interval):
input_range = Interval(input_range)
mean_input = (input_range.upper_bound + input_range.lower_bound) / 2
input_delta = (input_range.upper_bound - input_range.lower_bound) / 2
if model.inputs > 1:
mean_output = dc_gain(model) @ mean_input
output_delta = worst_case_peak_gain(model) @ input_delta
else:
mean_output = dc_gain(model) * mean_input
output_delta = worst_case_peak_gain(model) * input_delta
if model.outputs == 1:
mean_output = asscalar_if_possible(mean_output)
output_delta = asscalar_if_possible(output_delta)
a = mean_output - output_delta
b = mean_output + output_delta
return Interval(np.min([a, b], axis=0), np.max([a, b], axis=0))
def worst_case_peak_gain(model):
if not isinstance(model, sys.dlti):
model = sys.dlti(*model)
if isinstance(model, sys.StateSpaceDiscrete):
return WCPG_ABCD(model.A.astype(np.float64),
model.B.astype(np.float64),
model.C.astype(np.float64),
model.D.astype(np.float64))
if isinstance(model, sys.TransferFunctionDiscrete):
if model.outputs != 1:
raise NotImplementedError('SISO transfer functions only')
return worst_case_peak_gain(model.to_ss())[0, 0]
raise TypeError(f'Cannot compute worst case peak gain of {model}')
def dc_gain(model):
if not isinstance(model, sys.dlti):
model = sys.dlti(*model)
if isinstance(model, sys.ZerosPolesGainDiscrete):
model = model.to_tf()
if isinstance(model, sys.TransferFunctionDiscrete):
if model.outputs != 1:
raise NotImplementedError('SISO transfer functions only')
return np.sum(model.num) / np.sum(model.den)
if isinstance(model, sys.StateSpaceDiscrete):
return model.C @ np.linalg.inv(np.eye(*model.A.shape) -
model.A) @ model.B + model.D
raise TypeError(f'Cannot compute DC gain of {model}')
def is_stable(model, tol=1e-16):
if not isinstance(model, sys.dlti):
model = sys.dlti(*model)
return np.all(np.absolute(model.poles) < (1. - tol))