# ${\cal L}_{2}$ Gain of Periodic Linear Switched Systems: Fast Switching Behavior

@article{Roberson2009L,
title={\$\{\cal L\}_\{2\}\$ Gain of Periodic Linear Switched Systems: Fast Switching Behavior},
author={D. Gray Roberson and Daniel J. Stilwell},
journal={IEEE Transactions on Automatic Control},
year={2009},
volume={54},
pages={1632-1637}
}
We investigate the <i>L</i> <sub>2</sub> gain of periodic linear switched systems under fast switching. For systems that possess a suitable notion of a time-average system, we characterize the relationship between the <i>L</i> <sub>2</sub> gain of the switched system and the <i>L</i> <sub>2</sub> gain of its induced time-average system when the switching rate is sufficiently fast. We show that the switched system <i>L</i> <sub>2</sub> gain is in general different from the average system <i>L</i… CONTINUE READING