Youla parameterisation. Its special case is dead-beat control.
In addition to stability, as a fundamental condition for control systems, many other properties have to be controlled which have to meet the quality requirements of the operation. Such properties include operating costs, the speed and the accuracy of the desired settling process, filtering of unfavourable disturbances and noises. To this end, closed-loop control is usually extended with further elements that meet certain norms. At the same time, it must be ensured that these elements should not influence the stability of the system, as for example an element designed to reduce the settling time or costs can push the operating domain into this direction. Therefore, an element which does not influence stability must be independent from the controller, so the two elements should not have a common critical state. This condition, i.e. the exclusion of this common state, is fulfilled by coprime integers (by definition) in the world of numbers. The same condition can be set for analytic functions, as it can be calculated by relatively simple algorithms. This is the essence of the Youla–Kucera parametrisation. This result is marked as Q (for quality) in the figure.