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

  • Matrix-Tree Theorem
  • Lyapunov functions
  • Networks
  • Coupled systems
  • A graph-theoretic approach
  • Global stability

• Graduation date

  Fall 2010

• 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.