A contribution to the stability test for one-dimensional discrete time linear systems

The objective of this paper is to produce a general formulation of an order reduction procedure for testing the stability of discrete time linear systems. The order reduction procedure involves a series of iterations and, at each step of the iteration process, the aim is to derive a new polynomial of order lower than the given one. The new polynomial serves as the input to the following iteration. A specific form of the formulation is considered in which first order auxiliary polynomials are employed in the order reduction process. There follows from this a new testing procedure which is computationally more efficient than the existing ones. Moreover the current methods appear as special cases of the new test. An extension is further proposed which employs second order auxiliary polynomials within the order reduction formulation. This second order form is, however, for all practical cases the limit to which such a procedure can be put.