# step

Step response of dynamic system

## Syntax

## Description

`step`

computes the step response to a step change in input
value from *U* to *U* + *dU* after *t _{d}* time units.

Here,

*t*is the start time._{0}*t*is the step delay._{d}*t*is the final time._{f}*U*is the baseline input value.*dU*is the step amplitude.

By default, the function applies step for *t _{0}* =
0,

*U*= 0,

*dU*= 1, and

*t*= 0. But, you can configure these values using

_{d}`RespConfig`

. You can also specify the initial state
*x*(

*t*). When you don't,

_{0}`step`

assumes the system is initially at rest with input level
*U*.

`[`

computes the step response from `y`

,`tOut`

] = step(`sys`

,`[t0,tFinal]`

)`t0`

to `tFinal`

. For
response configurations with a step delay `td`

, the function applies the
step at time `t`

= `t0`

+ `td`

.* (since R2023b)*

`[`

specifies additional options for computing the step response, such as the step amplitude
(`y`

,`tOut`

] = step(`sys`

,___,`config`

)*dU*) or input offset (*U*). Use `RespConfig`

to create the option set `config`

. You
can use `config`

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

## Examples

## Input Arguments

## Output Arguments

## Tips

## Algorithms

To obtain samples of continuous-time models without internal delays,
`step`

converts such models to state-space models and discretizes them
using a zero-order hold on the inputs. `step`

chooses the sampling time for
this discretization automatically based on the system dynamics, except when you supply the
input time vector `t`

in the form `t = T0:dt:Tf`

. In that
case, `step`

uses `dt`

as the sampling time. The resulting
simulation time steps `tOut`

are equisampled with spacing
`dt`

.

For systems with internal delays, Control System Toolbox™ software uses variable step solvers. As a result, the time steps
`tOut`

are not equisampled.

## References

[1] L.F. Shampine and P. Gahinet, "Delay-differential-algebraic
equations in control theory," *Applied Numerical Mathematics*, Vol. 56,
Issues 3–4, pp. 574–588.

## Version History

**Introduced before R2006a**

## See Also

### Functions

`impulse`

|`RespConfig`

|`initial`

(Control System Toolbox) |`lsim`

|`stepplot`

### Apps

- Linear System Analyzer (Control System Toolbox)