# implicit_oneStepReachability

Computes one step of linear reachability analysis, as used by the linSys algorithm

## Contents

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

## Syntax

[Rtp, Rti, ctrl_variable, utotal, additional_variables, additional_constraints] = implicit_oneStepReachability(Rtp_previous, optsInternal)

## Description

Computes one step of linear reachability analysis, using the implicit approach for the controller. This entire algorithm is set up such that the reachability is computed symbolically, which is why we couldn't use CORA directly here.

## Input Arguments

Rtp_previous | Struct containing the symbolic variables describing the time-point solution from the previous step
optsInternal | Struct containing internal parameters

## Output Arguments

Rtp | Struct containing the symbolic variables describing the time-point solution
Rti | Struct containing the symbolic variables describing the time-interval solution
ctrl_variable | Struct containing the symbolic variables necessary to describe the controller
utotal | Struct containing the symbolic variables describing the input
additional_variables additional_constraints | These are the auxilliary variables and constraints that are needed to build the optimization problem, but don't necessarily have an interpretation.

## See Also

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## References

- *[1] "Approximability of the Containment Problem for Zonotopes and Ellipsotopes", A. Kulmburg et al., submited to TAC in 2024

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