A graphical test for the interval stability of fractional-delay systems

Abstract

This paper investigates the BIBO (bounded input and bounded output) interval stability testing of fractional-delay systems, a problem of justifying the BIBO stability of a polytopic family of functions involving fractional-order powers as well as exponential powers. It proves that the BIBO stability of the polytope is governed by the BIBO stability of the edges of the polytope, and the latter can be tested graphically via frequency response plots. The main results generalize some results in the literature.