Campus Units

Mathematics

Document Type

Article

Publication Version

Submitted Manuscript

Publication Date

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.

Comments

This is a manuscript of an article from IEEE Transactions on Automatic Control 58 (2013): 2349, doi:10.1109/TAC.2013.2250075. Posted with permission.

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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

Language

en

File Format

application/pdf

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