A unifying frame for stability-test algorithms for continuous-time systems

A number of stability-test algorithms for linear continuous-time systems are presented in a unified manner, which is based on a general recursive relation for generating a sequence of polynomials of descending degree. Each polynomial in the sequence is expressed as a suitable combination of the preceding polynomial of higher degree and the polynomial with opposite zeros. It is shown how the general recursion may give rise to the known stability-test algorithms as well as to some families of new algorithms. The corresponding criteria are proved with the aid of simple geometrical considerations based on root loci. In this way, insight is gained into the nature of the different procedures