Switching L2 gain for analyzing successive system switches*

In this paper, we consider a new switching $\mathcal{L}_{2}$ gain for evaluating the magnitude of successive system switches, and focus on its upper bound obtained simply as an analysis index. Furthermore, we simultaneously and simply design the initial states of newly-activated controllers at all system switches to establish the potential practicality as a design index of the upper bound. This is a novel approach to initial state design.