Critical parameters for a class of integral difference equations

Abstract

This contribution addresses the problem of calculating the critical parameters of a class of integral delay systems. The starting point of the analysis is a neutral-type system with distributed delay that results from the application of a differential operator, and whose spectrum contains the spectrum of the integral system. Based on recent results concerning the delay Lyapunov matrix for the class of obtained neutral-type systems, it is shown that the set of critical frequencies of the integral delay system is contained in the set of critical frequencies of a delay-free system of matrix equations. K E Y W O R D Scritical frequencies, delay-free system, integral difference equations, Lyapunov matrix, neutral systemswhere 𝛼 k,l ∈ R and k = 1, … , m.