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

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 cha...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2022-10, Vol.67 (10), p.5614-5621
Main Authors: Wu, Dongjun, Duan, Guang-Ren
Format: Article
Language:English
Subjects:
Asymptotic stability
Contraction analysis
Control theory
converse Lyapunov theorems
Geometry
Krasovskii’s method
Manifolds
Nonlinear Sciences
Riemann manifold
Riemannian manifold
Slot lines
Stability
Stability criteria
Theorems
Trajectory
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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2021.3122377