Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Optimization and Control

arXiv:2109.00974 (math)
[Submitted on 2 Sep 2021 (v1), last revised 25 May 2022 (this version, v2)]

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

Authors:Tim Mitchell, Paul Van Dooren
View PDF
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 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 to the setting of what we call root-max problems.
Comments: Revision #1
Subjects: Optimization and Control (math.OC); Systems and Control (eess.SY); Dynamical Systems (math.DS); Numerical Analysis (math.NA)
MSC classes: 93D09, 93C05, 49M15, 37J25
Cite as: arXiv:2109.00974 [math.OC]
  (or arXiv:2109.00974v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2109.00974

Submission history

From: Tim Mitchell [view email]
[v1] Thu, 2 Sep 2021 14:18:44 UTC (442 KB)
[v2] Wed, 25 May 2022 13:57:14 UTC (449 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.OC
< prev   |   next >
new | recent | 2021-09
Change to browse by:
cs
cs.NA
cs.SY
eess
eess.SY
math
math.DS
math.NA

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)