# Root-max Problems, Hybrid Expansion-Contraction, and Quadratically Convergent Optimization of Passive Systems

@article{Mitchell2021RootmaxPH, title={Root-max Problems, Hybrid Expansion-Contraction, and Quadratically Convergent Optimization of Passive Systems}, author={Tim Mitchell and Paul Van Dooren}, journal={ArXiv}, year={2021}, volume={abs/2109.00974} }

We present quadratically convergent algorithms to compute the extremal value of a real parameter for which a given rational transfer function of a linear time-invariant system is passive. This problem is formulated for both continuous-time and discrete-time systems and is linked to the problem of ﬁnding a realization of a rational transfer function such that its passivity radius is maximized. Our new methods make use of the Hybrid Expansion-Contraction algorithm, which we extend and generalize…

## One Citation

### On properties of univariate max functions at local maximizers

- MathematicsOptimization Letters
- 2022

More than three decades ago, Boyd and Balakrishnan established a regularity result for the two-norm of a transfer function at maximizers. Their result extends easily to the statement that the maximum…

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