ON THE MECHANISM OF RECURSIVE STABILITY-TEST ALGORITHMS

Most stability-test procedures are based on a recursion relation that, starting from a given characteristic polynomial, generates a sequence of polynomials P(i)(s) of descending degree i. The zero distribution with respect to the boundary of the stability region (the imaginary ax is, in the case of continuous-time systems) of each polynomial in the sequence is related to that of the preceding polynomial and to the val ue of a single parameter. To explain the operation of each method, the right-hand side P(i)(s) of the recursion is expressed as a suitable c ombination of the even and odd parts of P(i)(s), possibly multiplied b y low powers of s. It is shown how, for suitable values of the combina tion parameters, P(i)(s) admits a given factor R(s); the next polynomi al P(i)(s) in the sequence is obtained by factoring out R(s) from P(i) (s). This approach not only allows us to point out the common nature o f standard stability criteria but also to conceive new methods of comp arable complexity.