# 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*_{0}.

Continuous time:

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

Discrete time:

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

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

computes the response with initial state
*x*_{0}, initial parameter
*p*_{0} (LPV models), and input held to the offset
value (*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 Response Plots

`initial(`

plots
the unforced system response to initial states of a state-space (`sys`

,`x0`

)`ss`

) model `sys`

with an initial condition on the states
specified by the vector `x0`

:

The state-space model `sys`

can be continuous-time or
discrete-time, and SISO or MIMO. For MIMO state-space systems, the plot displays the
responses for the outputs of each channel. `initial`

automatically
determines the time steps and duration of the simulation based on the system
dynamics.

### Initial Response Data

## Examples

## Input Arguments

## Output Arguments

## Version History

**Introduced before R2006a**

## See Also

`initialplot`

| `impulse`

| `lsim`

| Linear System Analyzer | `step `