A Lyapunov-Based ISS Small-Gain Theorem for Infinite Networks of Nonlinear Systems

• 成果类型: Article
• 署名作者: Kawan, Christoph; Mironchenko, Andrii; Zamani, Majid
• 署名单位: University of Munich; University of Passau; University of Colorado System; University of Colorado Boulder
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3187949
• 发表日期: 2023
• 页码: 1447-1462
• 关键词: Stability criteria; Lyapunov methods; Power system stability; indexes; Finite element analysis; asymptotic stability; Sufficient conditions; infinite-dimensional systems; input-to-state stability; large-scale systems; Nonlinear systems; small-gain theorems

摘要

In this article, we show that an infinite network of input-to-state stable (ISS) subsystems, admitting ISS Lyapunov functions, itself admits an ISS Lyapunov function, provided that the couplings between the subsystems are sufficiently weak. The strength of the couplings is described in terms of the properties of an infinite-dimensional nonlinear positive operator, built from the interconnection gains. If this operator induces a uniformly globally asymptotically stable (UGAS) system, a Lyapunov function for the infinite network can be constructed. We analyze necessary and sufficient conditions for UGAS and relate them to small-gain conditions used in the stability analysis of finite networks.