Improvement of Polygo Interval Arithmetic and Evaluation of Value Sets of Transfer Functions of Uncertain Systems

Abstract

The purpose of this paper is to propose an improved version of inversion operation of Polygon Interval Arithmetic (PIA) and demonstrate the usefulness of it to evaluate value sets of control systems containing parameters whose values exist in given intervals but their exact values are not known. By using PIA, a polygon containing a value set as a subset is computed very fast. To get a good evaluation of the value set, it is required to express a given transfer function in a class of special forms. Two examples, which can be modified so that they belong to such a class, are presented. Since these expressions require to execute the inversion operation of PIA many times, to reduce the enlargement of the uncertainty caused by that, it is necessary to improve the definition of the inversion operation of PIA. Moreover, to implement the new inversion operation, an algorithm to decompose a non-convex polygons into convex polygons is proposed.