MIMO systems are only supported with sys_in as input argument.

Inputs

b

Numerator coefficients of continuous-time LTI system.

a

Denominator coefficients of continuous-time LTI system.

fs

Sampling frequency. If fs is not specified, or is an empty vector, it defaults to 1Hz. tol Tolerance of the internally used function minreal for canceling identical poles and zeros. If tol is not specified, it defaults to 0.0001 (0.1%).

sys_in

System definition of the continuous-time LTI system. This can also be a MIMO system.

Outputs

b_out

Numerator coefficients of the discrete-time impulse invariant LTI system.

a_out

Denominator coefficients of the discrete-time impulse invariant LTI system.

sys_out

Discrete-time impulse invaraiant LTI system. If sys_in is given as state space representation, sys_out is also returned in state space, otherwise as transfer function.

Algorithm

The step equivalent discretization of G(s) (zoh) results in G_zoh(z) = (z-1)/z * Z{G(s)/s} where Z{} is the z-transformation. The transfer function of the impulse equivalent discretization is given by T*Z{G(s)}. Therefore, the zoh discretizaiton method for s*G(s) multipled by T*z/(z-1) leads to the desired result.

Remark

For the impulse response of a discrete-time system, the input sequence {1/T,0,0,0,...} and not the unit impulse is considered. For this reason, the factor T is required for the impulse invaraint discretizaiton (see Algorithm).

See also: @lti/c2d

Source Code: imp_invar