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A semi analytic approach to the robust stability of quasipolynomials

Abstract A semi-analytic tool for the study of the robust stability of time delay systems is presented. The approach is based on graphical methods. The conditions of the Finite Nyquist Theorem for quasipolynomials given in (Santos et al. , 2003b) are improved. The Finite Inclusions Theorem for polytopic and interval quasipolynomials families is derived. An algorithm describing how to apply this new technique to analyze the robust stability of families of quasipolynomials is presented. The effectivity of this algorithm, which is implemented in Matlab, is validated with the analysis of two examples.