L2-gain analysis of regenerative switched linear systems with sampled-data state-feedback control

In this paper, we analyze the L
²
-gain of a class of switched linear systems under sampled-data state-feedback control. We consider switched linear systems whose switching signal is a regenerative process. Using the lifting approach and piecewise-constant approximations, we derive a sequence whose limit inferior upper-bounds the L
²
-gain of the closed-loop system. Each term of the sequence can be found by solving a linear matrix inequality. We illustrate the results by the L
²
-gain analysis of a linear system with a failure-prone controller.