Numerical aspects of linear control

Many physical systems evolve over time as a result of external and internal influences. They behave like black boxes: they receive an input, it is then transformed according to certain laws (usually a differential equation) and an output is observed. The problem is to regulate the input, to control it in order to obtain the desired output. Modifying the input according to the output obtained is called feedback. In French, this word is translated as retour, or looping, or rétroaction. Control theory studies such dynamic systems. When the output depends linearly on the input, we speak of linear control. When the output depends linearly on the input, it is referred to as linear control.

The basic idea behind linear control methods is to express a control problem as an optimization problem with an objective function that is linear and constraints that are linear matrix inequalities.