Letter to the Editor: Recursive Algorithms for Routh Test in Continuous and Discrete Time

Recursive Algorithms for Routh Test in Continuous and Discrete Time J, V. Wiseman In the design and analysis of linear control systems, one often needs to test the system's characteristic equation for roots in the right half of the complex s-plane (RHP). One such method is the Routh test and is of special importance in that it is simple and will indicate the number of RHP roots. With the advent of programmable calculators, recursive algorithms have come into popularity for solving relatively complex problems on calculators with the limited memory available. Presented herein are recursive algorithms developed by the author for performing the Routh test, axis shifting (for root searching), and the mapping: z = (s + l)/(s — 1) (for discrete time stability test). With the above recursions, the author has successfully Written a general program which will execute a 20th order polynomial, making the z = (s + l)/(s — 1) substitution, axis shift and Routh test, in less than 20 minutes on a hand held calculator.