Input–output finite time stabilization of linear systems

Bounded Input Bounded Output (BIBO) stability is usually studied when only the input–output behavior of a dynamical system is of concern. The present paper investigates the analogous concept in the framework of Finite Time Stability (FTS), namely the Input–Output FTS (IO-FTS). FTS has been already investigated in several papers in terms of state boundedness, whereas in this work we deal with the characterization of the input–output behavior. Sufficient conditions are given, concerning the class of L2L2 and L∞L∞ input signals, for the analysis of IO-FTS and for the design of a static state feedback controller, guaranteeing IO-FTS of the closed-loop system. The effectiveness of the proposed results is eventually illustrated by means of some numerical examples.