On singularly perturbed systems that are monotone with respect to a matrix cone of rank k

2023/03/21 by Ron Ofir, Ofir, Ron, Pietro Lorenzetti +3
Medicine · #Cardiovascular Disease and Adiposity #Cardiovascular Health and Disease Prevention #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2303.11970

openalex publication_date 2023/03/21 · openalex created_date 2023/03/23 · openalex updated_date 2026/07/28

Abstract

We derive a sufficient condition guaranteeing that a singularly perturbed linear time-varying system is strongly monotone with respect to a matrix cone C of rank k. This implies that the singularly perturbed system inherits the asymptotic properties of systems that are strongly monotone with respect to C, which include convergence to the set of equilibria when k=1, and a Poincaré-Bendixson property when k=2. We extend this result to singularly perturbed nonlinear systems with a compact and convex state-space. We demonstrate our theoretical results using a simple numerical example.

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