期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 58, 期 9, 页码 2349-2354出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2013.2250075
关键词
Control; graph; Lie algebra; quantum system; walk matrix; zero forcing
资金
- EPSRC [EP/F043678/1]
- NSF [ECCS0824085, DMS 0946431]
- EPSRC [EP/F043678/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/F043678/1] Funding Source: researchfish
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [946431] Funding Source: National Science Foundation
- Directorate For Engineering
- Div Of Electrical, Commun & Cyber Sys [824085] Funding Source: National Science Foundation
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.
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