A categorical approach to open and interconnected dynamical systems

Abstract

We develop a sound and complete graphical theory for discrete linear time-invariant dynamical systems. The graphical syntax, as in previous work, is closely related to the classical notion of signal flow diagrams, differently from previous work, these are understood as multi-input multi-output transducers that process streams with an \emph{infinite past} as well as an infinite future. This extended semantics features non-controllable systems, and we develop a novel, structural characterisation of controllability. Our approach is formalised through the theory of props, extending the work of Bonchi, Zanasi and the third author.