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

Yacine Chitour 1 Paolo Mason 1 Mario Sigalotti 2, 3
1 L2S - Laboratoire des signaux et systèmes
2 GECO - Geometric Control Design
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
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.
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https://hal.inria.fr/hal-01216017
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L2S | UNIV-PARIS-SACLAY | TDS-MACS | X-DEP-MATHA | CENTRALESUPELEC | SUP_SYSTEMES | CNRS | INRIA | X | INSMI | X-CMAP | CMAP | SUP_LSS

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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. ⟨10.1109/cdc.2015.7402985⟩. ⟨hal-01216017⟩

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