Algorithms for tree structured decomposition

Systems with tree structures can be checked extremely fast for stability by constructing their value sets. Often, such tree structures cannot be recognized easily in the transfer function or the characteristic polynomial of a system. For these cases, algorithms which make it possible to retrieve tree structures for polynomials and transfer functions are presented. The algorithms can be implemented within symbolic manipulation programs. Polynomials can be decomposed into sums or products of subpolynomials; transfer functions allow a continued fraction representation. The latter can also be used to determine a perturbation model which is frequently used in the robust control literature