A sectoring algorithm for exact computation of the frequency response of linear interval systems
This paper presents an algorithm for the computation of the frequency responses for linear interval systems. These are systems for which the transfer function \(G\) is not known precisely; instead intervals for the single coefficients appearing in the transfer function are known. For a given frequency \(\omega_0\) the frequency response is the set \(B\) of all complex values \(G(j\omega_0)\) for coefficients in the given intervals. In the algorithm the set \(B\) is represented via its boundary which is expressed as a concatenation of line segments and arcs. The algorithm consists of two steps: The first step is an ``elimination algorithm'' developed by the authors and \textit{C. Özdemir} [Circuits Syst. Signal Process. 15, No. 6, 735--748 (1996; Zbl 0874.93070)] which produces two sets (represented in the same way as \(B\)) based on the numerator and denominator of the transfer function. The desired set \(B\) is then given as the union of these two sets. In order to construct this union the second step is a ``sectoring algorithm'' which removes all those boundary lines of the two sets that do not belong to the boundary of the union. This part of the algorithm is the main contribution of the paper; it is presented in detail and illustrated by an example.
scientific article; zbMATH DE number 1234719
scientific article