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

Ian D. Morris

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arXiv · 2301.09942

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

Ian D. Morris

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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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Ian D. Morris. 2023-01-24. An irreducible linear switching system whose unique Barabanov norm is not strictly convex. https://arxiv.org/abs/2301.09942

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