Quotienting: A new perspective on the control of n-D systems

In this work, we investigate the process of quotienting the module of observables for a given n-D system by a suitable pre-defined submodule (obtained from a chosen ideal). We show that the functional meaning of this algebraic process is restricting the given n-D system, called the “plant,” to a special type of a smaller subsystem, called the “controlled system.” We further show that this controlled system can be independently characterized via a Malgrange-like duality result involving the above-mentioned process of quotienting. Finally, by proving an injectivity result, we show that this duality possesses a Galois connection, much akin to the conventional module-behaviour duality.