There exists a class of systems that is characterized by having a so called regular cellular structure or homogeneous interconnection. In this note, the bilateral Z-Transform is used to obtain a mathematical model parametrized by z and it is shown that the stability properties of the system can be more easily investigated by a simple test applied to the parametrized model. The analysis is illustrated via three examples: the heat equation, the Euler-Bernoulli beam, and decentralized control of a countably infinite string of interconnected mass-spring-damper systems.