An Abstract Block Formalism for Engineering Systems

We propose an abstract block diagram formalism based on the notions of a signal as a time-varying quantity, a block as a signal transformer, a connection between blocks as a signal equality constraint, and a block diagram as a collection of interconnected blocks. It does not enforce implementation details (like internal state-space) or particular kinds of dynamic behavior (like alternation of discrete steps and continuous evolutions) on blocks and can be considered as an abstraction of block diagram languages used by engineering system designers. We study its properties and give general conditions for well-definedness of the operation of a system specified by a block diagram for each admissible input signal(s).