Quasi-Barabanov Semigroups and Finiteness of the $L_2$-Induced Gain for Switched Linear Control Systems: Case of Full-State Observation - Archive ouverte HAL Access content directly
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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

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Yacine Chitour
Paolo Mason
Mario Sigalotti

#### 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.

### Dates and versions

hal-01216017 , version 1 (11-04-2020)

### Identifiers

• HAL Id : hal-01216017 , version 1
• DOI :

### Cite

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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