# approxAbsErrQuad_coefficients

coefficients of the quadratic approximation of the abstraction error.

## Contents

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

## Syntax

[quadCoeff,bilinCoeff,trCoeff] = approxAbsErrQuad_coefficients(obj,nlSys,termRegSet,W)

## Description

This function computes the coefficients of the quadratic approximation of the abstraction error proposed in [1, Proposition 1].

## Input Arguments

obj | instance of class computeTermRegNonlinSysLinApproach
nlSys | nonlinear system object (class: nonlinearSys / nonlinearSysDT)
termRegSet | candidate terminal region (class: zonotope)
W | set of disturbances (class: zonotope)

## Output Arguments

quadCoeff | coefficients of the quadratic terms [1, Eq. 27a] (array of dimension [obj.nx,1])
bilinCoeff | coefficients of the bilinear terms in [1, Eq. 27a] (array of dimension [obj.nx,1])
trCoeff | coefficients of the linear term, see [1, Eq. 27b] (array of dimension [obj.nx,1])

## See Also

@computeTermRegNonlinSysLinApproach/approxAbsErrQuad_eval

## References

[1] L. Schäfer et al. "Scalable Computation of Robust Control Invariant Sets of Nonlinear Systems", in IEEE Transactions on Automatic Control, vol. 69, no. 2, pp. 755-770, 2024

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