A generalized Kharitonov theorem for quasi-polynomials and entire functions occurring in systems with multiple and distributed delays

The classical Kharitonov theorem on interval stability cannot be carried over from polynomials to arbitrary entire functions. In this paper we identify a class of entire functions for which the desired generalization of the Kharitonov theorem can be proven. The class is wide enough to include classes quasi-polynomials occurring in the study of retarded systems with time delays, and some classes of entire functions that could be useful in studying systems with distributed delays. We also derive results for matrix polynomials and matrix entire functions.