Toward a Comprehensive Theory for Stability Regions of a Class of Nonlinear Discrete Dynamical Systems

• 成果类型: Article
• 署名作者: Dias, Elaine Santos; Costa Alberto, Luis Fernando; Amaral, Fabiolo Moraes; Chiang, Hsiao-Dong
• 署名单位: Universidade de Sao Paulo; Cornell University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3038271
• 发表日期: 2021
• 页码: 4371-4377
• 关键词: Asymptotic stability; stability analysis; Orbits; Power system stability; Numerical stability; dynamical systems; MANIFOLDS; Nonlinear discrete dynamical systems; periodic orbits; stability boundary; stability region

摘要

A comprehensive theory for the stability boundaries and the stability regions of a general class of nonlinear discrete dynamical systems is developed in this article. This general class of systems is modeled by diffeomorphisms and admits as limit sets only fixed points and periodic orbits. Topological and dynamical characterizations of stability boundaries are developed. Necessary and sufficient conditions for fixed points and periodic orbits to lie on the stability boundary are derived. Numerical examples, including applications to associative neural networks illustrating the theoretical developments, are presented.