Corpus ID: 237940658

The Barabanov norm is generically unique, simple, and easily computed

@inproceedings{Protasov2021TheBN,
  title={The Barabanov norm is generically unique, simple, and easily computed},
  author={Vladimir Yu. Protasov},
  year={2021}
}
Every irreducible discrete-time linear switching system possesses an invariant convex Lyapunov function (Barabanov norm), which provides a very refined analysis of trajectories. Until recently that notion remained rather theoretical apart from special cases. In 2015 N.Guglielmi and M.Zennaro showed that many systems possess at least one simple Barabanov norm, which moreover, can be efficiently computed. In this paper we classify all possible Barabanov norms for discrete-time systems. We prove… Expand

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References

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TLDR
A canonical procedure to construct them exactly is given, which associates a polytope extremal norm---constructed by using the methodologies described in Guglielmi, Wirth, and Zennaro (SIAM J. Matrix Anal. Math., 13 (2013), pp. 37--97)---to a polyTope Barabanov norm, which has the same genericity of an extremalpolytope norm. Expand
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TLDR
A new sufficient condition for this uniqueness is given, and a theoretical application shows that the property of having a unique Barabanov norm can in some cases be highly sensitive to small perturbations of the set of matrices. Expand
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