An Efficient Integer-Preserving Stability Test for Discrete-Time Systems

Abstract

The paper presents an efficient integer-preserving version for the author’s stability test for discrete-time linear systems. A first naive solution that satisfies this constraint is shown to have an explosive (severely exponential) growth of the magnitude of the integers. Then a simple, but far from obvious, new recursion form is established that has a more restrained (linear) growth of coefficients. A qualitative evaluation of computing time shows that the new test form is most efficient. Its possible usefulness for determining stability constraints for filters and systems with designable parameters is illustrated by a numerical example. Its capacity to offer better numerical accuracy for high-degree polynomials is also illuminated. Additional applications may arise from its usability over other algebraic rings. The latter capacity was demonstrated recently by implementing it into an efficient stability test for two-dimensional discrete-time systems.