Input-Output Finite-Time Stability

This paper introduces the extension of FiniteTime Stability (FTS) to the input-output case, namely the Input-Output FTS (IO-FTS). The main differences between classic IO stability and IO-FTS are that the latter involves signals defined over a finite time interval, does not necessarily require the inputs and outputs to belong to the same class of signals, and that quantitative bounds on both inputs and outputs must be specified. This paper revises some recent results on IO-FTS, both in the context of linear systems and in the context of switching systems. In the final example the proposed methodology is used to minimize the maximum displacement and velocity of a building subject to an earthquake of given magnitude.