Enhanced TDS stability analysis method via characteristic quasipolynomial polynomization

Abstract

Time delay systems own infinite spectra which cannot be simply analyzed or controlled. A way how to deal with this task consists of an approximation of the characteristic quasipolynomial by a polynomial that can be further handled via conventional tools. This contribution is aimed at an improved extrapolation method transforming a retarded quasipolynomial into a corresponding polynomial. It is equivalent to the finding of a finite-dimensional model related to an infinite-dimensional one describing a time delay system. The approximating polynomial is then used to analyze the dependence of delay values to exponential stability of the system. Two ideas are adopted and compared here; namely, a linear interpolation method via the Regula Falsi method, and the root Newton’s method with root tendency. The whole procedure is simply implementable by using standard software tools. To demonstrate this issue, a numerical example performed in MATLAB® & Simulink® environment is given to the reader. © Springer International Publishing AG 2017.