The Meaning of Structure in Interconnected Dynamic Systems

Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces the complete computational structure of a system as a common baseline for comparing different simplified representations. Linear systems are then used as a vehicle for comparing and contrasting distinct partial structure representations. Such representations simplify the description of a system's complete computational structure at various levels of fidelity while retaining a full description of the system's input-output dynamic behavior. Relationships between these various partial structure representations are detailed, and the landscape of new realization, minimality, and model reduction problems introduced by these representations is briefly surveyed.