On Special Quadratic Lyapunov Functions for Linear Dynamical Systems with an Invariant Cone

Omri Dalin, Alexander Ovseevich, Michael Margaliot

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a continuous-time linear time-invariant dynamical system that admits an invariant cone. For the case of a self-dual and homogeneous cone we show that if the system is asymptotically stable then it admits a quadratic Lyapunov function with a special structure. The complexity of this Lyapunov function, in terms of the number of parameters defining it, scales linearly with the dimension of the dynamical system. In the particular case when the cone is the nonnegative orthant this reduces to the well-known and important result that a positive system admits a diagonal Lyapunov function. We demonstrate our theoretical results by deriving a new special quadratic Lyapunov function for systems that admit the ice-cream cone as an invariant set.

Original languageEnglish
Pages (from-to)1-6
Number of pages6
JournalIEEE Transactions on Automatic Control
DOIs
StateAccepted/In press - 2024

Keywords

  • Dynamical systems
  • Lie algebra
  • Lie group
  • Linear systems
  • Lyapunov methods
  • Reviews
  • special Lyapunov functions
  • stability analysis
  • Stability analysis
  • Symmetric matrices
  • Vectors

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