Generalized Energy Functions for a Class of Third-Order Nonlinear Dynamical Systems

• 成果类型: Article
• 署名作者: Costa Alberto, Luis Fernando; Siqueira, Daniel S.; Bretas, Newton Geraldo; 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.2020.3029316
• 发表日期: 2021
• 页码: 3111-3122
• 关键词: Power system stability; stability analysis; nonlinear dynamical systems; asymptotic stability; Lyapunov methods; trajectory; Orbits; Energy function; generalized energy function; Nonlinear systems; stability of nonlinear systems

摘要

Nonlinear dynamical systems exhibiting complex structure in their limit sets, such as chaotic and closed orbits, do not admit energy functions. The theory of generalized energy functions, which may assume positive derivative in some bounded sets, appears as an alternative to study the asymptotic behavior of solutions of these systems. In this article, a generalized energy function and a complete characterization of the stability boundary and stability region are developed for a class of third-order dynamical systems. This class of systems appears in electrical power system models and has a class of quasi-gradient systems and second-order systems as particular cases. These systems may admit complex structure in their limit sets and do not admit an energy function that is general for the class. Numerical examples illustrate how generalized energy functions provide estimates of stability regions.