Switched systems that are periodically stable may be unstable

Blondel, Vincent;Theys, Jacques;Vladimirov, A.A.
(2002) MTNS-02: 15th International Symposium on Mathematical Theory of Networks and Systems — Location: Notre Dame, IN, USA (12.August.2002)

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  • Blondel, Vincentorcid-logoUCLouvain
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  • Theys, JacquesUCLouvain
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  • Vladimirov, A.A.
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Abstract
We prove the existence of two 2*2 real matrices such that all periodic products of these matrices converge to zero but there exists an infinite product that does not. We outline implications of this result for the stability of switched linear systems, and for the finiteness conjecture.
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Blondel, V., Theys, J., & Vladimirov, A. A. (2002). Switched systems that are periodically stable may be unstable. In Gilliam, D.S.; Rosenthal, J.; (ed.), Proceedings Fifteenth International Symposium on Mathematical Theory ofNetworks and Systems (p. p. 1-6). Univ. notre dame. https://hdl.handle.net/2078.5/230419