Input to Output Finite-Time Stabilization of Discrete-Time Linear Systems

Bounded–Input Bounded–Output (BIBO) stability is usually studied when only the input-output behavior of a dynamical system is of interest. 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. A system is said to be input-output finite time stable if, assigned a class of input signals and some boundaries in the output signal space, the output never exceeds such boundaries over a prespecified (finite) interval of time. This paper provides some sufficient conditions 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 two numerical examples.