Application of LaSalle's Invariance Principle on Polynomial Differential Equations Using Quantifier Elimination

• 成果类型: Article
• 署名作者: Gerbet, Daniel; Roebenack, Klaus
• 署名单位: Technische Universitat Dresden
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3103887
• 发表日期: 2022
• 页码: 3590-3597
• 关键词: Asymptotic stability; dynamical systems; control theory; MANIFOLDS; geometry; Autonomous systems; tools; Invariance Principle; algebraic geometry; quantifier elimination

摘要

LaSalle's invariance principle is a commonly used extension of Lyapunov's second method to study asymptotic stability of nonlinear systems. If the system can be written in polynomial form, the examination can be automated using algebraic geometry and quantifier elimination. This article addresses this automated examination using a method relying on polynomial ideals and applies it on some example systems. In addition, some properties of these special ideals are derived that allow to reduce the computational effort significantly.