The determination of root loci using Routh's algorithm

Root-locus algorithms for microcomputers

“…Hence, branchfollowing programs invariably require a considerable amount of 'special' programming in order to avoid the various problems which can arise. proposed by Bendrikov and Teodorchk (1963) and later developed by Chen and Hsu (1966) as an area-search routine. The method is based on two principles, namely that a Routh array can be used to determine the location of pure imaginary roots and also that the configuration of a root-locus diagram is independent of any linear co-ordinate transformation.…”

“…Area-search methods (Chen and Hsu, 1966;Hennci, 1974) involve the specification of a grid covering a defined area in the s-plane. Each point in the grid is then systematically tested to find those satisfying necessary and sufficient conditions for the existence of a root locus.…”

Routh’s Algorithm: A Centennial Survey

“…Finally, the original Routh algorithm can be used to compute the continued fraction expansion for twovariable rational functions [38]. Nevertheless, we have not been exhaustive (e.g., [15]) and doubtless other uses remain to be discovered. Concluding remarks.…”