AN IRREDUCIBLE LINEAR SWITCHING SYSTEM WHOSE UNIQUE BARABANOV NORM IS NOT STRICTLY CONVEX.

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 Chitour, Gaye, and Mason. [ABSTRACT FROM AUTHOR]