ピボッティングによる根軌跡の計算アルゴリズム

抄録

A numerical algorithm to obtain root-loci of linear time-invariant control systems is proposed. The algorithm is based on the homotopy method to solve general nonlinear equations. The complex plane is divided into small triangles. Each vertex of the triangles is obtained sequentially. The sequence of specially labelled triangles gives an approximation of the root-loci. The procedure to find triangles with a special set of labels is called pivoting. Two propositions are given to validate the algorithm. The first one guarantees that the algorithm never fails in the vicnity of branching points of root-loci if the size of the triangulation of the complex plane is taken sufficiently small. The second proposition gives the precision of the approximation. The precision depends mainly on the size of triangles. Finally, the efficiency of the method is shown by several examples.