1. Objective and modeling

The first step is to formalize the problem at hand mathematically: this is the subject of this section. After specifying the class of systems under consideration, the control objective is formulated and the two main approaches to achieving it are defined. The emulation approach is then pursued and a final complete model with both continuous-time dynamics specific to the physical system (between two successive transmission instants) and discrete instantaneous behaviors (corresponding to data transmission) is presented. The terms "transmission" and "sampling" are used interchangeably to designate the transmission of data between the system and its controller and/or the updating of the latter.