General and split forms of some well-known s-domain algorithms

A common frame for some well-known algorithms for the stability analysis of continuous-time linear systems is derived. Specifically, a general polynomial recursion is given which includes as particular cases both Routh- and Levinson-type algorithms and is capable of generating new algorithms too. A systematic analysis of all possible corresponding split forms (three-term immittance-domain recurrence relations) is then carried out. This may allow one to clarify and compare the properties of the standard procedures.