We propose a new switching gain for evaluating the fluctuations in transient responses after an unpredictable switch, such as a switch caused by a failure in a control device occurring in the normal operation, between two linear time-invariant systems. We also present gain conditions that enable us to compute the value of the proposed switching gain. We then theoretically establish its applicability as an analysis index. Furthermore, by applying the proposed gain to switching matrix design, we show its potential applicability as a design index.