Global stability analysis for stochastic coupled systems on networks

• DOI: 10.1016/j.automatica.2010.10.041
• Publication Date: 2010-11-24T09:25:40Z
• Authors: Wenxue Li; Huan Su; Ke Wang
• Keywords: Lyapunov stability; Stability theory

This paper considers the global stability problem for some stochastic coupled systems on networks (SCSNs). We provide a systematic method for constructing a global Lyapunov function for these SCSNs, by using graph theory and the Lyapunov second method. Consequently, a new global stability principle, which has a close relation to the topology property of the network, is given. As an application to the results, we employ the principle to two well-known coupled systems in physical and ecology, and then some easy-verified sufficient conditions which guarantee the global stability are obtained.