Simulation relations for discrete-time linear systems

Simulation relations of labeled transition systems are used in theoretical computer science in order to formally establish notions of modeling abstraction and refinement in hierarchical systems. In this paper, we establish and characterize simulation relations for arbitrary discrete-time, linear control systems. More precisely, given two discrete-time systems, we consider various embeddings into labeled transition systems, that differ in the amount of timing information that is maintained in the transition relation. For each embedding, we obtain necessary and sufficient conditions for one discrete-time system simulating the transitions of the other. Naturally, the simulation characterizations become weaker as more information is abstracted away in the embedding.