Testing Stability of 2-D Discrete Systems by a Set of Real 1-D Stability Tests

Abstract

Stability of a two-dimensional (2-D) discrete system depends on whether a bivariate polynomial does not vanish in the closed exterior of the unit bi-circle. The paper shows a procedure that tests this 2-D stability condition by testing the stability of a finite collection of real univariate polynomials by a certain modified form of the author's one-dimensional (1-D) stability test. The new procedure is obtained by telepolation (interpolation) of a 2-D tabular test whose derivation was confined to using a real form of the underlying 1-D stability test. Consequently, unlike previous telepolation-based tests, the procedure requires the testing of real instead of complex univariate polynomials. The proposed test is the least-cost procedure to test 2-D stability with real polynomial 1-D stability tests and real arithmetic only.