Conditions for finiteness of a constructive algorithm for determining stability

In earlier papers [1], [2], a methodology for deciding on the stability of a system of nonlinear differential equations was proposed. This methodology reduced the problem to a test of boundedness of all finite products of a given finite set of matrices. This paper investigates further the issue of whether the algorithm will terminate in finitely many steps and obtains some new conditions, concentrating on the case where the system being tested is unstable.