Switching $\mathcal{L}_{2}$ Gain for Evaluating the Fluctuations Around an Output of a Specified Transfer Property

In this paper, we introduce the difference structure to pre- and post-switch systems, to propose a new switching L
2
gain for evaluating the fluctuations around an output of a specified transfer property after a system switch. Moreover, we apply it to the initial state design of a newly-activated controller designed by model matching to establish its potential practicality as a design index.