An irreducible linear switching system whose unique Barabanov norm is not strictly convex

2023/01/24 by Ian D. Morris, Morris, Ian D.
Engineering · Mathematics · #34a38 93c30 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2301.09942

openalex publication_date 2023/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a marginally stable linear switching system in continuous time, in four dimensions and with three switching states, which is exponentially stable with respect to constant switching laws and which has a unique Barabanov norm, but such that the Barabanov norm fails to be strictly convex. This resolves a question of Y. Chitour, M. Gaye and P. Mason.

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