# Gain Scheduled Lead-Lag

Implement first-order lead-lag with gain-scheduled coefficients

GNC/Controls

## Description

The Gain Scheduled Lead-Lag block implements a first-order lag of the form

`$u=\frac{1+as}{1+bs}e$`

where e is the filter input, and u the filter output.

The coefficients a and b are inputs to the block, and hence can be made dependent on flight condition or operating point. For example, they could be produced from the Lookup Table (n-D) Simulink® block.

## Parameters

Initial state, x_initial

The initial internal state for the filter `x_initial`. Given this initial state, the initial output is given by

`${u|}_{t=0}=\frac{x_initial+ae}{b}$`

## Inputs and Outputs

InputDimension TypeDescription

First

Contains the filter input.

Second

Contains the numerator coefficient.

Third

Contains the denominator coefficient.

OutputDimension TypeDescription

First

Contains the filter output.