A reliable stability test for exponential polynomials

The investigation of the stability of an exponential polynomial is a well-known problem in the literature. Although exact analytic conditions to check stability are known, they are often too difficult to check, certainly in practical problems. Therefore mostly a graphical test is used, based on the well-known circle-criterion. In this paper an algorithmization of such a test is presented. Although the method can be applied to low order exponential polynomials, it is especially suitable to test the stability of high order exponential polynomials, often needed for the stabilization of time-delay systems. The method proposed in this paper is designed to carry out this test in a reliable and efficient way. Key Words: Exponential polynomials, Stability, Circle-criterion, Variable step-length, Curvature.