Non-delay parameter depending stability of a time-delay system

Abstract

A characteristic equation of a time-delay system contains a quasipolynomial rather then a polynomial. Solutions of the equation, system poles, have as the same meaning as for delay-free systems, thus they decide about system stability. This contribution studies the influence of a non-delay real parameter in a selected characteristic quasipolynomial to time-delay system stability. The analysis is based on the argument principle which also holds for the selected quasipolynomial. Upper and lower stability bounds for the parameter are found through proven lemmas, propositions and theorems.