# approxAbsErrQuad_eval

evaluates the quadratic approximation of the abstraction error.

## Contents

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

## Syntax

approxAbsErr = approxAbsErrQuad_eval(var_dzquad,var_exploitTR,quadCoeff,bilinCoeff,trCoeff)

## Description

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

## Input Arguments

var_dzquad | squared semi-edge lengths of interval enclosing the Cartesian product of the terminal region, the set of admissible control inputs and the set of disturbances (array of dimension [nx+nu+nw,1])
var_exploitTR | scalar measuring the exploitation of the trust region, see [1, Eq. 28a]
quadCoeff | coefficients of the quadratic terms [1, Eq. 27a] (array of dimension [nx,1])
bilinCoeff | coefficients of the bilinear terms in [1, Eq. 27a] (array of dimension [nx,1])
trCoeff | coefficients of the linear term, see [1, Eq. 27b] (array of dimension [nx,1])

## Output Arguments

approxAbsErr | (lower bound of) abstraction error approximation (non-negative array of dimension [nx,1])

## See Also

@computeTermRegNonlinSysLinApproach/approxAbsErrQuad_coefficients

## 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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