ℒ2-induced gains of switched systems and classes of switching signals

This paper addresses the ℒ₂-induced gain analysis for switched linear systems. We exploit non-conservative necessary and sufficient conditions for the induced gain to lie below a prescribed positive constant and discuss on the induced gains of switched systems obtained for different classes of switching signals, which distinct regularity assumptions are placed on. We particularly show that the induced gain that is obtained for the class of every piecewise constant switching signal can also be attained by the more restricted classes of switching signals.