# Varying State Space

State-space model with varying matrix values

**Libraries:**

Control System Toolbox /
Linear Parameter Varying

## Description

Use this block to implement a continuous-time state-space model with varying
matrices. Feed the instantaneous values of the state matrix *A*, input
matrix *B*, output matrix *C*, and feedforward matrix
*D* to the corresponding input ports. The system response is given
by:

$$\begin{array}{c}dx=Ax+Bu\\ y=Cx+Du,\end{array}$$

where *u* is the system input, *y* is the system
output, and *x* and *dx* are the state vector and
state derivatives, respectively.

Use this block and the other blocks in the Linear Parameter Varying library to implement common control elements with variable parameters or coefficients. For more information, see Model Gain-Scheduled Control Systems in Simulink.

**Caution**

Avoid making the **C** and **D** matrices depend
on the system output **y**. If you have such dependence, the
resulting state-space equation *y* =
*C*(*y*)*x* +
*D*(*y*)*u* creates an algebraic loop, because computing the output value
*y* requires knowing the output value. This algebraic loop is
prone to instability and divergence. Instead, try expressing **C**
and **D** in terms of the time *t*, the block
input **u**, and the state outputs **x**.

For similar reasons, avoid making **A** and
**B** depend on the **dx** output. Note that
it is safe for **A** and **B** to depend on
**y** when **y** is a fixed combination of
states and inputs (in other words, when *y* = *C**x* +
*D**u*, where *C* and *D* are constant
matrices).

## Ports

### Input

### Output

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2017b**