Conditions of Self-Oscillations in Generalized Persidskii Systems

• 成果类型: Article
• 署名作者: Wang, Jian; Avila, Jesus Mendoza; Efimov, Denis; Aleksandrov, Alexander; Fridman, Leonid
• 署名单位: Hangzhou Dianzi University; Universidad Nacional Autonoma de Mexico; Saint Petersburg State University; Centre National de la Recherche Scientifique (CNRS); Universite de Lille; Inria; ITMO University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3066581
• 发表日期: 2022
• 页码: 1514-1520
• 关键词: Lyapunov methods; oscillators; stability analysis; nonlinear dynamical systems; trajectory; Robustness; Sliding mode control; Linear matrix inequalities; Lyapunov methods; nonlinear control systems

摘要

For a class of generalized Persidskii systems, whose dynamics are described by superposition of a linear part with multiple sector nonlinearities and exogenous perturbations, the conditions of practical stability, instability, and oscillatory behavior in the sense of Yakubovich are established. For this purpose, the conditions of local instability at the origin and global boundedness of solutions (practical input-to-state stability) are developed in the form of linear matrix inequalities. The proposed theory is applied to investigate robustness to unmodeled dynamics of nonlinear feedback controls in linear systems, and to determine the presence of oscillations in the models of neurons.