Computation of Gain Margin Using Polygon Interval Arithmetic

Abstract

In this paper, a method to compute almost exact gain margin of uncertain control systems using Polygon Interval Arithmetic (PIA) is proposed. The main problem here is to determine 0-exclusion property of the value set of the characteristic polynomial. By using PIA, we can compute the convex hull of the value set very fast. When we need a better estimate of the value set, we need to split a region of uncertain parameters : however, the method to decide which region should be split was not given, and it may require very large computing time to get a good estimate. In this paper, we confine ourselves to the case when an expression of characteristic polynomial which corresponds to a totally decomposable tree structure decomposition is given, and we propose a method to decide which region should be split. By adopting this method, we Can compute a good estimate in a short time.