Contraction Analysis of Monotone Systems via Separable Functions

Kawano, Y., Besselink, B. & Cao, M., Aug-2020, In : IEEE-Transactions on Automatic Control. 65, 8, p. 3486-3501 16 p., 8854175.

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In this paper, we study incremental stability of monotone nonlinear systems through contraction analysis. We provide sufficient conditions for incremental asymptotic stability in terms of the Lie derivatives of differential one-forms or Lie brackets of vector fields. These conditions can be viewed as sum- or max-separable conditions, respectively. For incremental exponential stability, we show that the existence of such separable functions is both necessary and sufficient under standard assumptions for the converse Lyapunov theorem of exponential stability. As a by-product, we also provide necessary and sufficient conditions for exponential stability of positive linear time-varying systems. The results are illustrated through examples.

Original languageEnglish
Article number8854175
Pages (from-to)3486-3501
Number of pages16
JournalIEEE-Transactions on Automatic Control
Issue number8
Publication statusPublished - Aug-2020


  • Control theory, Asymptotic stability, Stability analysis, Nonlinear systems, Eigenvalues and eigenfunctions, Linear systems, Contraction analysis, monotone systems, nonlinear systems, separable functions, LYAPUNOV FUNCTIONS, STABILITY ANALYSIS, CRITERIA, METRICS, MODEL

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