Contraction Analysis of Monotone Systems via Separable Functions

Yu Kawano*, Bart Besselink, Ming Cao

*Bijbehorende auteur voor dit werk

OnderzoeksoutputAcademicpeer review

1 Citaat (Scopus)
46 Downloads (Pure)


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.

Originele taal-2English
Pagina's (van-tot)3486-3501
Aantal pagina's16
TijdschriftIEEE-Transactions on Automatic Control
Nummer van het tijdschrift8
StatusPublished - aug-2020

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