# Quasi-Barabanov Semigroups and Finiteness of the $L_2$-Induced Gain for Switched Linear Control Systems: Case of Full-State Observation

2 GECO - Geometric Control Design
Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : Motivated by an open problem posed by J.P. Hespanha we extend the notion of Barabanov norm and extremal trajectory to general classes of switching signals. As a consequence we characterize the finiteness of the L2-induced gain for a large set of switched linear control systems in case of full-state observation in terms of the sign of the generalized spectral radius associated with minimal realizations of the original switched system.
Type de document :
Communication dans un congrès
54th IEEE Conference on Decision and Control (CDC), Dec 2015, Osaka, Japan. Proceedings of the 54th IEEE Conference on Decision and Control. 〈10.1109/cdc.2015.7402985 〉
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https://hal.inria.fr/hal-01216017
Contributeur : Mario Sigalotti <>
Soumis le : jeudi 15 octobre 2015 - 14:14:00
Dernière modification le : jeudi 10 mai 2018 - 02:03:58

### Citation

Yacine Chitour, Paolo Mason, Mario Sigalotti. Quasi-Barabanov Semigroups and Finiteness of the $L_2$-Induced Gain for Switched Linear Control Systems: Case of Full-State Observation. 54th IEEE Conference on Decision and Control (CDC), Dec 2015, Osaka, Japan. Proceedings of the 54th IEEE Conference on Decision and Control. 〈10.1109/cdc.2015.7402985 〉. 〈hal-01216017〉

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