Determining the closest stable polynomial to an unstable one

Abstract

The problem of being given a polynomial whose zeros do not all lie on or inside the unit circle and finding the closest polynomial whose zeros are all on or inside the unit circle is considered. The measure of closeness used is the weighted Euclidean distance in coefficient space. The algorithm can be extended to other measures of closeness as well. Because the direct minimization on the coefficient space is difficult, the problem is approached in Schur coefficient space. In this way, the stability condition is easily guaranteed. A very efficient algorithm for obtaining the optimum solution is developed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>