Laplacian Dynamics on Cographs: Controllability Analysis Through Joins and Unions

• 成果类型: Article
• 署名作者: Mousavi, Shima Sadat; Haeri, Mohammad; Mesbahi, Mehran
• 署名单位: Sharif University of Technology; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Washington; University of Washington Seattle
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2992444
• 发表日期: 2021
• 页码: 1383-1390
• 关键词: Controllability; Laplace equations; Eigenvalues and eigenfunctions; Protocols; Electrical engineering; tree graphs; biology; Cographs; Laplacian dynamics; network controllability; threshold graphs

摘要

In this article, we examine the controllability of Laplacian dynamic networks on cographs. Cographs appear in modeling a wide range of networks and include as special instances, the threshold graphs. In this article, we present necessary and sufficient conditions for the controllability of cographs, and provide an efficient method for selecting a minimal set of input nodes from which the network is controllable. In particular, we define a sibling partition in a cograph and show that the network is controllable if all nodes of any cell of this partition except one are chosen as control nodes. The key ingredient for such characterizations is the intricate connection between the modularity of cographs and their modal properties. Finally, we use these results to characterize the controllability conditions for certain subclasses of cographs.