Rapid Methods for the Solution of Automatic Control Equations

In automatic control and other branches of engineering it is frequently necessary to find the roots of an algebraic equation. One of the authors has presented iteration methods for solving for both real and complex roots by right-to-left synthetic division. These methods are convergent for many, but not all, classes of roots. This paper presents a study of the convergence of the methods and extends the methods to cover the regions of nonconvergence. In addition, an improved array is presented for checking the Routh-Hurwitz stability criterion. The use of the methods in analysis and design of automatic control systems is demonstrated by numerical examples.