An analysis stability test for a certain class of distributed parameter systems with delays

The aim of this paper is to apply an algebraic test such as the Routh algorithm, Hurwitz determinant, or any similar method to a certain class of distributed parameter systems with multiple delays. As a first step, an auxiliary system is generated, and then two auxiliary polynomials are formed by using only the coefficients of the characteristic equation of the auxiliary system. The input-output stability of the original system is determined on the basis of the zero distribution of two auxiliary polynomials. An illustrative example is included.