Most of the systems in modern-day engineering applications are governed by either partial differential/difference equations (n-D systems) or delay-differential equations. Such systems can be modeled as infinite dimensional dynamical systems. A crucial question regarding the dynamical systems defined over an infinite dimensional state-space is that of stability. However, as the underlying state-space is infinite dimensional, generalization of results about the stability of finite dimensional systems is not straightforward and can be counter-intuitive.

In this talk, we examine a particular family of infinite dimensional discrete autonomous systems, which are governed by a Laurent polynomial matrix in the shift operator. We call this family of systems as Laurent systems. A Laurent system emerges in many interesting scenarios - namely, time-relevant discrete 2-D systems, the formation problem of infinite chains of agents, repetitive processes encountered in coal-cutting and metal-rolling industries, discrete quantum mechanics, etc. Moreover, the stability analysis of Laurent systems is closely related to the stability analysis of discrete 2-D autonomous systems (i.e., autonomous systems governed by partial difference equations in two independent variables). In this talk, we compare four different notions of stability for Laurent systems, and explain how some of the stability results are counter-intuitive when compared with the case of finite dimensional systems. We also discuss its application to the formation problem of infinite chains of agents (vehicles/drones/sensors).