# linearBackwardReach

backward reachable set for linearized system

## Contents

- Syntax
- Description
- Input Arguments
- Output Arguments
- See Also
- References

## Syntax

[R,H] = linearBackwardReach(goalSet,xCenter,uCenter,U,Opts)

## Description

This function computes the backward reachable set starting from the goal set for the inearized system.

## Input Arguments

goalSet | goal set that should be reached (class: zonotope)
xCenter | cell-array containing the reference trajectory states for all intermediate time steps
uCenter | cell-array containing the reference trajectory inputs for all intermediate time steps
U | cell-array containing the sets of admissble control inputs for all intermediate time steps
Opts | structure containing the following options
.Ninter | number of intermediate time steps
.nu | number of inputs
.nw | number of disturbances
.dt | time step size for one intermediate time step
.funHandle | function handle for the dynamic function
.linDyn.A | function handle to the system matrix of the linearize dynamics
.linDyn.B | function handle to the input matrix of the linearize dynamics

## Output Arguments

R | backward reachable set (class: zonotope)
H | matrix storing the generator-to-input assignment

## See Also

`safetyNetControl`

## References

- [1] Schuermann et al. (2019), Formal Safety Net Control Using Backward Reachability Analysis

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