Towards automatic design of multi domain high level systems through interval arithmetics

To design a system the designer has to establish equations of performances over available adjustments. These equations are non linear, implicit or explicit, static or dynamic with no reversal form. The game is to find an efficient method to determine the good value of adjustments in order to respect restrictions on performances (or specifications). These methods are domain specific and often tiresome and unwieldy. We show in this paper there exists an other point of view on this general problem with the help of a branch of mathematics: the arithmetic of intervals.