BUILT-IN MATHEMATICA SYMBOL

# OutputResponse

OutputResponse[sys, u, {t, tmin, tmax}]
gives the numeric output response of system sys to the input u for .

OutputResponse[sys, {u[0], u[1], ...}]
gives the output response of the discrete-time system sys to the input sequence .

OutputResponse[sys, u, t]
gives the symbolic output response of system sys to the input u as a function of time t.

OutputResponse[sys, {u1, ..., um}, ...]
gives the output response to for multiple inputs .

## DetailsDetails

• OutputResponse is also known as impulse response, step response, and ramp response.
• OutputResponse solves the underlying differential or difference equations for the given input.
• The systems model sys can be a StateSpaceModel or a TransferFunctionModel.
• The initial values for the differential and difference equations are taken to be zero unless specified.
• OutputResponse[{ssm, {x10, x20, ..., xn0}}, ...] can be used to specify the initial state for a StateSpaceModel ssm.
• For descriptor state-space systems, the initial states need to be consistent.
• For delay state-space systems, the initial states include history and can be given as for t≤0. »

## ExamplesExamplesopen allclose all

### Basic Examples (4)Basic Examples (4)

The step response of a second-order system:

 Out[1]=

The output response of a transfer-function model to a sinusoidal input:

 Out[1]=

Visualize the response:

 Out[2]=

The response of a state-space model from nonzero initial conditions:

 Out[1]=
 Out[2]=

The response of a discrete-time system to a sampled sinusoid:

 Out[1]=
 Out[2]=