Picard's method to solve a system of biaffine equations and its application to pole placement

Abstract

Picard's method for finding the roots of univariate polynomials has been extended to solve multivariate biaffine equations. It is shown that from the same initial guess, the proposed method finds most of the real solutions of a set of biaffine equations. Method's applicability in solving constrained state and output feedback pole placement problems is demonstrated through numerical examples. The main advantage of this method is that it provides a systematic way of finding more than one solutions of a given set of equations.