Qualitative equivalence of dynamical systems with applications to discrete event systems

Stability preserving mappings are used to identify general dynamical systems having equivalent qualitative properties. The authors establish sufficient conditions for a mapping to have stability preserving properties and they use stability preserving mappings to formulate comparison theorems for general dynamical systems. The results developed include most of the corresponding comparison results reported in the literature as special cases. In addition, the present results are applicable to certain classes of general dynamical systems, such as discrete event systems, which cannot be addressed by corresponding previous results. For such systems, the motions which make up a dynamical system are not determined by equations, as is required by the existing results. The applicability of the results developed is demonstrated on a class of discrete event systems