Robust stability of quasipolynomials with commensurate delays

Abstract

In this paper we study the robust stability of uncertain quasipolynomials, whose coefficients are only known to be confined within certain prescribed sets. We consider such quasipolynomials with commensurate delays. We derive a sufficient condition for the uncertain quasipolynomials to be robustly stable independent of delay, when they are confined to the families of interval, diamond, and spherical quasipolynomials. The condition requires checking the robust stability of one polynomial, and computing additionally a frequency-dependent matrix.