A NORMALIZED SCHUR-COHN STABILITY TEST FOR THE DELTA-OPERATOR-BASED POLYNOMIALS

Two delta-operator-based stability: tests, or more generally zero loca tion tests. were recently proposed in a separate paper. Those tests es tablish two families of such tests, each spanning from the discrete-ti me to the continuous-time with the delta operator providing smooth tra nsitions between the two domains. In this paper a third family is prop osed. Specifically, the normalized Schur-Cohn test in the discrete-tim e domain is transformed into the delta-operator domain resulting in a new delta-operator test. The limit of this new test as the sampling in terval vanishes is shown to be the recent Pham-Le Breton test in the c ontinuous-time domain. Its relationships with the well-known Routh tes t and others are studied. A numerical example shows the advantage of t he new test for fast sampling.