# initial

System response to initial states of state-space model

## Syntax

## Description

For state-space and sparse state-space models, `initial`

computes the unforced system response *y* to initial states
*x _{init}*.

Continuous time:

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

Discrete time:

$$\begin{array}{cc}x[k+1]=Ax[k]& x[{k}_{0}]={x}_{init}\\ y=Cx[k]& \end{array}$$

For linear time-varying or linear parameter-varying state-space models,
`initial`

computes the response with initial state
*x _{init}*, initial parameter

*p*(LPV models), and input held to the offset value (

_{init}*u*(

*t*) =

*u*

_{0}(

*t*) or

*u*(

*t*) =

*u*

_{0}(

*t*,

*p*). This corresponds to the initial condition response of the local linear dynamics.

`initial(`

plots the initial response of `sys`

,`xinit`

,___)`sys`

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

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

instead.

## Examples

## Input Arguments

## Output Arguments

## Version History

**Introduced before R2006a**

## See Also

`initialplot`

| `impulse`

| `lsim`

| Linear System Analyzer | `step `