Characterizations of Global Transversal Exponential Stability

• 成果类型: Article
• 署名作者: Andrieu, Vincent; Jayawardhana, Bayu; Praly, Laurent
• 署名单位: Universite Claude Bernard Lyon 1; Centre National de la Recherche Scientifique (CNRS); University of Groningen; Universite PSL; MINES ParisTech
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3036021
• 发表日期: 2021
• 页码: 3682-3694
• 关键词: Manifolds; control theory; STABILITY; Lyapunov methods; asymptotic stability; measurement; trajectory; contraction; exponentially attractive invariant manifold; transversal exponential stability

摘要

We study the relationship between the global exponential stability of an invariant manifold and the existence of a positive semidefinite Riemannian metric which is contracted by the flow. In particular, we investigate how the following properties are related to each other (in the global case): 1) A manifold is globally transversally exponentially stable; 2) the corresponding variational system admits the same property; 3) there exists a degenerate Riemannian metric which is contracted by the flow and can be used to construct a Lyapunov function. We show that the transverse contraction rate being larger than the expansion of the shadow on the manifold is a sufficient condition for the existence of such a Lyapunov function. An illustration of these tools is given in the context of global full-order observer design.