Switching ℒ₂ gain for evaluating the fluctuations in transient responses after an unpredictable system switch

Abstract

We propose a new switching L2 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 L2 gain conditions that enable us to compute the value of the proposed switching L2 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.