Further Geometric and Lyapunov Characterizations of Incrementally Stable Systems on Finsler Manifolds

• 成果类型: Article
• 署名作者: Wu, Dongjun; Duan, Guang-Ren
• 署名单位: Harbin Institute of Technology; Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3122377
• 发表日期: 2022
• 页码: 5614-5621
• 关键词: Stability criteria; asymptotic stability; MANIFOLDS; trajectory; geometry; control theory; Slot lines; Contraction analysis; converse Lyapunov theorems; Krasovskii's method; Riemannian manifold

摘要

In this article, we report several new geometric and Lyapunov characterizations of incrementally stable systems on Finsler and Riemannian manifolds. A new and intrinsic proof of an important theorem in contraction analysis is given via the complete lift of the system. Based on this, two Lyapunov characterizations of incrementally stable systems are derived, namely, converse contraction theorems, and revelation of the connection between incremental stability and stability of an equilibrium point, in which the second result recovers and extends the classical Krasovskii's method.