Title :
A Differential Lyapunov Framework for Contraction Analysis
Author :
Forni, F. ; Sepulchre, R.
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Univ. of Liege, Liège, Belgium
Abstract :
Lyapunov´s second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves.
Keywords :
Lyapunov methods; differential equations; stability; state-space methods; Finsler structure; Lyapunov second theorem; analog theorem; differential Lyapunov framework; differential equations; incremental stability analysis; infinitesimal contraction; state-space; tangent bundle; Asymptotic stability; Differential equations; Lyapunov methods; Manifolds; Measurement; Stability analysis; Vectors; Contraction; Lyapunov methods; incremental stability; linearization; nonlinear systems;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2013.2285771
