English

Exact Volume of Zonotopes Generated by a Matrix Pair

Systems and Control 2020-04-14 v1 Systems and Control Optimization and Control

Abstract

In this article, we define a class of special zonotopes generated by a matrix pair with finite-interval parameters. We discuss the relationship between the volume of these zonotopes and the controllability of one aspect (the volume of the controllable region) of the dynamic systems. We present a corollary and develop an effective recursive method to compute the volume of the special zonotopes. Furthermore, we develop two recursive and analytical volume-computation methods for the finite- and infinite-time controllable regions with real eigenvalues. We conduct numerical experiments to demonstrate the effectiveness of these new volume-computation methods for zonotopes and regions.

Cite

@article{arxiv.2004.05530,
  title  = {Exact Volume of Zonotopes Generated by a Matrix Pair},
  author = {Mingwang Zhao},
  journal= {arXiv preprint arXiv:2004.05530},
  year   = {2020}
}

Comments

20 pages, 3 tables

R2 v1 2026-06-23T14:48:19.653Z