Input-output finite-time stability of linear systems

Abstract

When only the input-output behavior of a dynamical system is of concern, usually Bounded-Input Bounded-Output (BIBO) stability is studied, for which several results exist in literature. The present paper investigates the analogous concept in the framework of Finite Time Stability (FTS), namely the Input-Output FTS. A system is said to be IO finite time stable if, assigned a bounded input class and some boundaries in the output signal space, the output never exceeds such boundaries over a prespecified (finite) interval of time. FTS has been already investigated in several papers in terms of state boundedness, whereas this is the first work dealing with the characterization of the input-output behavior. Sufficient conditions are given, concerning the class of L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> 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. Finally, the applicability of the results is illustrated by means of two numerical examples.