Stability of differential equations via the theory of continued fraction expansions (Q1382742)

The author presents two systems of differential equations. The first system is a stable continuous time system i.e. all roots of the characteristic equation lie in the left half of the complex plane, and the second is a stable discrete time system, i.e. the roots of the characteristic equation lie in the unit circle. The characteristic polynomial is expressed as a sum of two functions whose ratio is expanded in terms of a general function. Using this representation, the author constructs a continued fraction expansion related to both systems. An example demonstrating the idea is presented. This article is rich of references to this subject.