Algebraic Preliminaries

Abstract

This chapter provides a brief introduction to partially ordered sets (posets), lattices, the lattice of equivalence relations, and derived concepts such as the factorization of a function through its equivalence kernel. These ideas capture, in a primitive but useful way, the general notion of ‘information’ in a feedback control loop together with that of ‘dynamic observer’ by which such information is extracted. An application is sketched to the Internal Model Principle of regulation theory, in a relatively unstructured setting of plain sets and functions.

The original version of this chapter was revised: Belated corrections have been incorporated. The correction to this chapter is available at https://doi.org/10.1007/978-3-319-77452-7_10