# reachControlledLTISystem

compute reachable sets for controlled LTI system

## Contents

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

## Syntax

[R,auxTerm] = reachControlledLTISystem(Opts,R0,inpSets,Rpar,Rtran)

## Description

This function computes reachable sets for controlled linear time-invariant systems. We consider additional terms required for the multiplication of a zonotope and a interval matrix separately to ensure convexity of the subsequent optimization problem, because abs(abs(X)) terms are problematic.

## Input Arguments

Opts | a structure containing following options
.TpOrTi | compute reachable sets at time point only (Opts.TpOrTi = `'Tp'`) or also the time interval reachable sets (Opts.TpOrTi = `'Ti'`)
.N | number of time-steps until safe terminal set is reached starting in safe initial set
.XKX | feedback matrix for the extended system dynamics
.taylor | struct containing the propagation matrices for the linear system
R0 | initial set (given by Z-matrix storing center; and generators)
inpSets | multidimensional array storing the centers and generators of the input correction zonotopes
Rpar | particluar solution due to uncertain inputs
Rtrans | particular solution due to constant inputs

## Output Arguments

R | cell-array containing overall reachable sets
auxTerm | cell-array containing auxiliary terms required for the constraints

## See Also

`computeTermRegZonoLinSys`

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