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Article
Zero Forcing, Linear and Quantum Controllability for Systems Evolving on Networks
IEEE Transactions on Automatic Control
  • Daniel Burgarth, Aberystwyth University
  • Domenico D'Alessandro, Iowa State University
  • Leslie Hogben, Iowa State University
  • Simone Severini, University College London
  • Michael Young, Iowa State University
Document Type
Article
Disciplines
Publication Version
Accepted Manuscript
Publication Date
9-1-2013
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 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.

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Copyright Owner
IEEE
Language
en
File Format
application/pdf
Citation Information
Daniel Burgarth, Domenico D'Alessandro, Leslie Hogben, Simone Severini, et al.. "Zero Forcing, Linear and Quantum Controllability for Systems Evolving on Networks" IEEE Transactions on Automatic Control Vol. 58 Iss. 9 (2013) p. 2349 - 2354
Available at: http://works.bepress.com/leslie-hogben/43/