Rootmax Problems, Hybrid ExpansionContraction, and Quadratically Convergent Optimization of Passive Systems
Abstract
We present quadratically convergent algorithms to compute the extremal value of a real parameter for which a given rational transfer function of a linear timeinvariant system is passive. This problem is formulated for both continuoustime and discretetime 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 ExpansionContraction algorithm, which we extend and generalize to the setting of what we call rootmax problems.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.00974
 Bibcode:
 2021arXiv210900974M
 Keywords:

 Mathematics  Optimization and Control;
 Electrical Engineering and Systems Science  Systems and Control;
 Mathematics  Dynamical Systems;
 Mathematics  Numerical Analysis;
 93D09;
 93C05;
 49M15;
 37J25
 EPrint:
 Revision #1