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