# computeTermRegZonoLinSys

compute terminal region with linear system approach using zonotopes

## Contents

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

## Syntax

T = computeTermRegZonoLinSys(benchmark,Param,Opts)

## Description

This function computes a terminal region with the linear system approach in [1].

## Input Arguments

benchmark | name of the considered benchmark model (see; "aroc/benchmarks/dynamics/...")
Param | a structure containing the benchmark parameters
.U | set of admissible control inputs (class: interval)
.W | set of uncertain disturbances (class: interval)
.X | set of state constraints (class: interval)
Opts | a structure containing following options
.Tdomain | search domain for the terminal region (class:; interval)
.xEq | states for the equibrium point of the system
.uEq | control inputs for the equilibrium point of the system
.timeStep | time step size for the sampled data controller [positive scalar]
.N | number of time steps [{10}, positive integer]
.K | feedback matrix for the terminal contorller
.Q | state weighting matrix for the LQR approach applied to determine the terminal controller [{eye(nx)} / positive-definite square matrix]
.R | input weighting matrix for the LQR approach applied to determine the terminal controller [{zeros(nu)} / positive-definite square matrix]
.maxDist | maximum distance for convergence criterion [{1e-2} / positive scalar]
.genMethod | method for computing the fixed generator matrix for the terminal set [{`'termSet'`} / `'sampling2D'`, `'provided'`]
.G | generator matrix for the terminal set (for; Opts.genMethod = `'provided'` only)
.costFun | cost function used for the optimization problem [{`'geomean'`} / `'sum'`, `'none'`]
.cora.taylorTerms | taylor order for computing e^At [{4} / positive integer]
.cora.zonotopeOrder | maximum zonotope order [{150} / positive integer]

## Output Arguments

T | object of class termRegZonoLinSys

## See Also

`terminalRegion`, `termRegZonoLinSys`

## References

- [1] 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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