Investigation of Behavior and Synthesis of Interval Dynamic Systems' Characteristic Polynomials Based on the Root Locus Portrait Parameter Function
А. А. Несенчук · 2018
Investigation of the 4thpower dynamic systems behavior in conditions of the interval parameter variations is carried out on the basis of root locus portraits. The behavior regularities at the system asymptotic stability boundary are determined for root locus portraits of the 4thpower systems with interval parametric uncertainties. On this basis the stability conditions are derived and expressions are determined for calculating intervals of characteristic polynomial family parameters' variation ensuring the system robust stability. It further develops results represented in the papers of B.D.O. Anderson and V.L. Kharitonov where they consider issues of analysis and synthesis of robust polynomial families. Unlike it is stated by B.D.O. Anderson and V.L. Kharitonov who offer to apply for checking interval systems' family stability correspondingly two (for the 4thpower systems) and four polynomials of the system characteristic polynomial family with constant coefficients, in this paper it is stated that for the 4thpower interval systems' families asymptotic stability analysis it is enough to use only one polynomial of this kind. Moreover, the discovered regularities of the system root locus portrait behavior allow to extract stable sub-families from the unstable families of interval system characteristic polynomials and to determine, whether there exists at least one stable polynomial in the unstable polynomial family.