Stability analysis of monotone systems via max-separable Lyapunov functions

H. R. Feyzmahdavian, B. Besselink, M. Johansson

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We analyze stability properties of monotone nonlinear systems via max-separable Lyapunov functions, motivated by the following observations: first, recent results have shown that asymptotic stability of a monotone nonlinear system implies the existence of a max-separable Lyapunov function on a compact set; second, for monotone linear systems, asymptotic stability implies the stronger properties of D-stability and insensitivity to time delays. This paper establishes that for monotone nonlinear systems, equivalence holds between asymptotic stability, the existence of a max-separable Lyapunov function, D-stability, and insensitivity to bounded and unbounded time-varying delays. In particular, a new and general notion of D-stability for monotone nonlinear systems is discussed, and a set of necessary and sufficient conditions for delay-independent stability are derived. Examples show how the results extend the state of the art.
Original languageEnglish
Pages (from-to)643-656
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number3
Publication statusPublished - Mar-2018


  • Asymptotic stability
  • Delays
  • Linear systems
  • Lyapunov methods
  • Nonlinear systems
  • Stability criteria
  • D-stability
  • Delay systems
  • monotone systems
  • positive systems

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