Campus Units
Mathematics, Electrical and Computer Engineering
Document Type
Article
Publication Version
Accepted Manuscript
Publication Date
9-2013
Journal or Book Title
IEEE Transactions on Automatic Control
Volume
58
Issue
9
First Page
2349
Last Page
2354
DOI
10.1109/TAC.2013.2250075
Abstract
We study the dynamics of systems on networks from a linear algebraic perspective. The control theoretic concept of controllability describes the set of states that can be reached for these systems. Our main result says that controllability in the quantum sense, expressed by the Lie algebra rank condition, and controllability in the sense of linear systems, expressed by the controllability matrix rank condition, are equivalent conditions. We also investigate how the graph theoretic concept of a zero forcing set impacts the controllability property; if a set of vertices is a zero forcing set, the associated dynamical system is controllable. These results open up the possibility of further exploiting the analogy between networks, linear control systems theory, and quantum systems Lie algebraic theory. This study is motivated by several quantum systems currently under study, including continuous quantum walks modeling transport phenomena.
Rights
Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Copyright Owner
IEEE
Copyright Date
2013
Language
en
File Format
application/pdf
Recommended Citation
Burgarth, Daniel; D'Alessandro, Domenico; Hogben, Leslie; Severini, Simone; and Young, Michael, "Zero Forcing, Linear and Quantum Controllability for Systems Evolving on Networks" (2013). Mathematics Publications. 61.
https://lib.dr.iastate.edu/math_pubs/61
Comments
This is a manuscript of an article published as Burgarth, Daniel, Domenico D'Alessandro, Leslie Hogben, Simone Severini, and Michael Young. "Zero forcing, linear and quantum controllability for systems evolving on networks." IEEE Transactions on Automatic Control 58, no. 9 (2013): 2349-2354. DOI: 10.1109/TAC.2013.2250075. Posted with permission.