Sufficient Conditions for Robust Input-Output Finite-Time Stability of Linear Systems in Presence of Uncertainties

The concept of Bounded-Input Bounded-Output (BIBO) stability arises when one wants to focus on the study of the the input-output behavior of a dynamical system, as opposed to the classical Lyapunov stability. 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. IO-FTS has been already investigated in previous papers, whereas this is the first work dealing with the input-output behavior of an uncertain dynamical system in the FTS framework. Two sufficient conditions are given, concerning the class of 2 and ∞ input signals, for the analysis of robust IO-FTS. The applicability of the results is illustrated by means of a numerical examples.