DERIVATION OF RECURSIVE STABILITY-TEST PROCEDURES

The classical zero-location procedures (in their so-called two-term sc attering-type form) essentially consist of a recursion that allows us to obtain a polynomial P(i-1) (s) of degree i-1 from the current polyn omial P(i) (s) of degree i, and to relate the distribution of the zero s of P(i) (s) to that of P(i-1) (s) and to the value of a real paramet er. This approach provides a simple interpretation of the standard alg orithms and suggests criteria for generating new equivalent algorithms . Specifically, it is shown that the general structure of the recursio n uses a suitable combination of the even and odd parts of P(i) (s) ac cording to two parameters. Each particular procedure corresponds to a straight line in the parameter plane, which amounts to imposing a cons traint on the considered parameters, so that only one of them can be u sed as the current coordinate along the line. It is shown how the prop erties of P(i-1) (s) depend on die position of the associated point in the parameter plane.