# Varying Transfer Function

Transfer function with varying coefficients

**Libraries:**

Control System Toolbox /
Linear Parameter Varying

## Description

This block implements a continuous-time transfer function with varying coefficients. The instantaneous transfer function is given by:

$$H\left(s\right)=\frac{{b}_{0}+{b}_{1}{s}^{-1}+\cdots +{b}_{N}{s}^{-N}}{1+{a}_{1}{s}^{-1}+\cdots +{a}_{N}{s}^{-N}}=\frac{{b}_{0}{s}^{N}+{b}_{1}{s}^{N-1}+\cdots +{b}_{N}}{{s}^{N}+{a}_{1}{s}^{N-1}+\cdots +{a}^{N}}.$$

*N* is number of poles, specified with the **Transfer
function order** parameter. Feed the values of the coefficients *b*_{0},
*b*_{1},…,
*b _{N}* and

*a*

_{1},

*a*

_{2},…,

*a*

_{N}to the corresponding block input ports.

**Note**

The above expression for *H*(*s*) applies only
to Varying Transfer Function blocks added to a model in R2023a or
later. For information about Varying Transfer Function blocks created
in R2022b or earlier, see Varying Transfer Function block formula changed.

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 transfer-function coefficients depend on the block output
**y**. If you have such dependence, the resulting transfer
function causes an algebraic loop, because computing the block output value requires
knowing the block output value. This algebraic loop is prone to instability and
divergence. Instead of the output, try expressing the coefficients in terms of the
time *t* and the block input **u**.

## Ports

### Input

### Output

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2017b**