Remarks on redundance in stability criteria and a counterexample to fullers conjecture

Abstract It is shown that the [n(n+ l)/2] conditions for stability in the left-half plane as well as inside the unit circle as given by Routh and Jury-Gutman, can be reduced reapectively to {[n[n− 1)/2] + l} and {[n[n− 1)/2] + 2} conditions. Furthermore, a counter example of sixth degree polynomial to Fuller's conjecture of n-conditions is obtained. Finally, methods for obtaining polynomials for root-pair-sums, root-pair-product and polynomials having as roots the negative of squares of root-pair-differences (needed for aperiodicity conditions are obtained.