# ltvss

## Description

Use `ltvss`

to represent linear state-space models whose dynamics
vary with time.

You can use `ltvss`

to create continuous-time or discrete-time linear
time-varying state-space models. In continuous time, an `ltvss`

model is
described by the following state-space equations.

$$\begin{array}{c}E(t)\dot{x}={\delta}_{0}(t)+A(t)(x-{x}_{0}(t))+B(t)(u-{u}_{0}(t))\\ y(t)={y}_{0}(t)+C(t)(x-{x}_{0}(t))+D(t)(u-{u}_{0}(t))\end{array}$$

Here, *A*(*t*),
*B*(*t*), *C*(*t*),
*D*(*t*), and *E*(*t*)
are time-varying state-space matrices and
*δ*_{0}(*t*),
*x*_{0}(*t*),
*u*_{0}(*t*), and
*y*_{0}(*t*) are time-dependent
derivative, state, input, and output offsets, respectively.

In discrete time, an `ltvss`

model is described by the following
state-space equations.

$$\begin{array}{c}{E}_{k}{x}_{k+1}={\delta}_{0k}+{A}_{k}({x}_{k}-{x}_{0}{}_{k})+{B}_{k}({u}_{k}-{u}_{0}{}_{k})\\ {y}_{k}={y}_{0k}+{C}_{k}({x}_{k}-{x}_{0}{}_{k})+{D}_{k}({u}_{k}-{u}_{0}{}_{k})\end{array}$$

Here, the integer index *k* counts the number of sampling periods
`Ts`

.

You can use an `ltvss`

object to model:

Linear systems whose coefficients vary in time.

Nonlinear systems operating along a specific trajectory. For an example, see LTV Model of Two-Link Robot.

Nonlinear systems operating near steady-state conditions that change in time.

Use `ltvss`

to construct LTV models whose dynamics are described by a
MATLAB^{®} function (the *data function*). Use `ssInterpolant`

to
construct LTV models that interpolate LTI snapshots as a function of time. See LPV and LTV Models for functions and
operations applicable to `ltvss`

objects.

## Creation

### Syntax

### Description

creates a continuous-time LTV model. `ltvSys`

= ltvss(`DataFcn`

)`DataFcn`

is the name of or a
handle to the *data function*, the user-defined MATLAB function that calculates the matrices and offsets for given
*t* or *k* values.

sets properties of the linear time-varying model using one or more name-value pair
arguments. Use this syntax with any of the previous input-argument combinations.`ltvSys`

= ltvss(___,`Name=Value`

)

### Input Arguments

## Properties

## Object Functions

## Examples

## Version History

**Introduced in R2023a**