# impulse

Impulse response plot of dynamic system; impulse response data

## Syntax

## Description

`[`

computes the response from `y`

,`tOut`

] = impulse(`sys`

,`[t0,tFinal]`

)`t0`

to `tFinal`

. For
response configurations `config`

with an impulse delay
`td`

, the function applies the impulse at time `t`

=
`t0`

+ `td`

.* (since R2023b)*

`[`

specifies additional options for computing the impulse response, such as the amplitude or
input offset. Use `y`

,`tOut`

] = impulse(___,`config`

)`RespConfig`

to create the option set `config`

. You
can use `config`

with any of the previous input-argument and
output-argument combinations.

`impulse(`

plots the
impulse response of `sys`

,___)`sys`

. This syntax is equivalent to
`impulseplot(sys,__)`

. When you need additional plot customization
options, use `impulseplot`

instead.

## Examples

## Input Arguments

## Output Arguments

## Limitations

The impulse response of a continuous system with nonzero

*D*matrix is infinite at*t*=*0*.`impulse`

ignores this discontinuity and returns the lower continuity value*Cb*at*t*=*0*.The

`impulse`

command does not work on continuous-time models with internal delays. For such models, use`pade`

(Control System Toolbox) to approximate the time delay before computing the impulse response.The

`impulse`

command does not support simulation along an implicit parameter trajectory for continuous-time LPV models.

## Tips

When you need additional plot customization options, use

`impulseplot`

instead.To simulate system responses to arbitrary input signals, use

`lsim`

.

## Algorithms

Continuous-time LTI models are first converted to state-space form. The impulse response of a single-input state-space model

$$\begin{array}{l}\dot{x}=Ax+bu\\ y=Cx\end{array}$$

is equivalent to the following unforced response with initial state
*b*.

$$\begin{array}{cc}\dot{x}=Ax,& x(0)=b\\ y=Cx& \end{array}$$

To simulate this response, the system is discretized using zero-order hold on the inputs.
The sample time is chosen automatically based on the system dynamics, except when a time
vector `t = T0:dt:Tf`

is supplied. Hence, `dt`

is used as
sample time.

## Version History

**Introduced before R2006a**

## See Also

Linear System Analyzer (Control System Toolbox) | `step`

| `lsim`

| `impulseest`

| `pade`

(Control System Toolbox) | `impulseplot`