On the stability of real exponential polynomials with interval-valued delays

We consider the family ? of exponential polynomials. $$f_T (z): = f_0 (z) + f_1 (z)e^{ - zT_1 } + f_2 (z)e^{ - T_2 } + \cdots + f_n (z)e^{ - zT_n } ,T : = T_1 \times T_2 \times \cdots \times T_n ,$$ where thef _k(z),k=0(1)n, are real polynomials under the degree restriction deg(f ₀)>deg(f _k),k=1(1)n, and theT _k,k=1(1)n, are intervals inR ₊. The functions in ? are characteristic functions of linear, retarded dynamical systems with constant coefficients and finitely many interval-valued discrete delays. A stability criterion for ? is expounded; ? is stable if (a) ? contains a stable member and (b) a certain functionalT:S(y) →; {0, 1} vanishes fory in a compact interval inR ₊. Here,S(y) is the boundary of a circular are regionS(y) in the complex plane derived fromf _T. Tools needed for a computer implementation are compiled.