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A graph-theoretic approach to the construction of Lyapunov functions for coupled systems on networks

  • Author / Creator
    Shuai, Zhisheng
  • For coupled systems of differential equations on networks, a graph-theoretic approach to the construction of Lyapunov functions is systematically developed in this thesis. Kirchhoff’s Matrix-Tree Theorem in graph theory plays an essential role in the approach’s development. The approach is successfully applied to several coupled systems well-known in the literature to demonstrate its applicability and effectiveness.

  • Subjects / Keywords
  • Graduation date
    2010-11
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3B14T
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Mathematical and Statistical Sciences
  • Supervisor / co-supervisor and their department(s)
    • Li, Michael (Mathematical and Statistical Sciences)
    • Berger, Arno (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Muldowney, James (Mathematical and Statistical Sciences)
    • Marquez, Horacio (Electrical and Computer Engineering)
    • Han, Bin (Mathematical and Statistical Sciences)
    • Wang, Hao (Mathematical and Statistical Sciences)
    • Smith, Hal (Mathematical and Statistical Sciences, Arizona State University)