# termReglinSys

terminal region object computed with the approaches proposed in [1] and [2]

## Contents

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

## Syntax

obj = termReglinSys(dynamics, termReg, termReg_zono, termRegState, termRegState_zono, termSet, Rtp, R, s, termRegCtrl, debug, runtimes, optsInternal)

## Description

This class represents a terminal region computed with the approach in [1] and [2].

## Input Arguments

dynamics | function handle to the dynamic function of the open loop system
termReg | terminal region (class: zonotope or ellipsoid)
termReg_zono | zonotopic terminal region
termRegState | terminal region of the state (class: zonotope or; ellipsoid)
termRegState_zono | zonotopic terminal region of the state
termSet | terminal safe set, for the `'fixed'` approach
Rtp | over-approximations of the reachable set at time steps i * Opts.timeStep, for i=0,...,Opts.N
R | over-approximation of the reachable set of termReg, assuming each point is steered using the control inputs from termRegCtrl
s | value of the initial stretching factors
termRegCtrl | set-based safety-presevering controller
runtimes | struct containing information about the runtimes of the different parts of the algorithm
optsInternal | a structure containing internal algorithm settings See ./src/cLS_setOptsInternal

## Output Arguments

obj | resulting object of class termRegContainmentLinSys

## See Also

`terminalRegion`, `computeTermRegNonlinSysLinApproach`

## References

- *[1] "Approximability of the Containment Problem for Zonotopes and Ellipsotopes", A. Kulmburg et al., submited to TAC in 2024
- [2] Gruber et al. (2021), Computing safe sets of linear sampled-data systems, IEEE Control Syst. Lett., vol. 5, no. 2, pp. 385-390

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