Input-Output Finite-Time Stability

TL;DR

This paper extends the concept of finite-time stability to input-output systems, providing new theoretical results and practical methods for controlling system responses within finite time bounds, especially in the context of linear and switching systems.

Contribution

It introduces Input-Output Finite-Time Stability (IO-FTS), broadening the stability analysis to finite-time input-output signals and providing revised results for linear and switching systems.

Findings

Revised theoretical results on IO-FTS for linear systems

Application of IO-FTS to minimize building displacement during earthquakes

Methodology allows for finite-time bounds on inputs and outputs

Abstract

This paper introduces the extension of Finite-Time 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.