scipy.signal.lsim(system, U, T, X0=None, interp=True)[source]

Simulate output of a continuous-time linear system.


system : an instance of the LTI class or a tuple describing the system.

The following gives the number of elements in the tuple and the interpretation:

  • 1: (instance of lti)
  • 2: (num, den)
  • 3: (zeros, poles, gain)
  • 4: (A, B, C, D)

U : array_like

An input array describing the input at each time T (interpolation is assumed between given times). If there are multiple inputs, then each column of the rank-2 array represents an input. If U = 0 or None, a zero input is used.

T : array_like

The time steps at which the input is defined and at which the output is desired. Must be nonnegative, increasing, and equally spaced.

X0 : array_like, optional

The initial conditions on the state vector (zero by default).

interp : bool, optional

Whether to use linear (True, the default) or zero-order-hold (False) interpolation for the input array.


T : 1D ndarray

Time values for the output.

yout : 1D ndarray

System response.

xout : ndarray

Time evolution of the state vector.


If (num, den) is passed in for system, coefficients for both the numerator and denominator should be specified in descending exponent order (e.g. s^2 + 3s + 5 would be represented as [1, 3, 5]).


Simulate a double integrator y’’ = u, with a constant input u = 1

>>> from scipy import signal
>>> system = signal.lti([[0., 1.], [0., 0.]], [[0.], [1.]], [[1., 0.]], 0.)
>>> t = np.linspace(0, 5)
>>> u = np.ones_like(t)
>>> tout, y, x = signal.lsim(system, u, t)
>>> import matplotlib.pyplot as plt
>>> plt.plot(t, y)

(Source code)