Algebraic algorithm for stability testing of discrete systems and its application to stability testing of 2 dimensional systems

摘要

Some improvements have been proposed for a Bose's 2D(2 dimensional) stability test by revealing symmetric properties of the polynomials and the resultant in the test. We first show that Schussler's 1D stability criterion can be tested with the complexity of computation in largely reduced as it involves only certain real variable polynomials with degrees not exceeding half of their previous counterparts. Based on Schussler's 1D stability criterion, Bose has developed a resultant-based stability test for 2D systems. Using above result and the property that the resultant is selt-inversive, we give an improved version of the Bose's 2D stability test. The proposed 2D stability test can be fulfilled more efficiently by totally algebraic algorithm and can be implemented more easily and systematically into a 2D CAD system. Non-trivial examples have also been shown.