  In this paper, we propose a new approach to prove stability of non-linear
discrete-time systems. After introducing the new concept of stability
contractor, we show that the interval centred form plays a fundamental role in
this context and makes it possible to easily prove asymptotic stability of a
discrete system. Then, we illustrate the principle of our approach through
theoretical examples. Finally, we provide two practical examples using our
method : proving stability of a localisation system and that of the trajectory
of a robot.

Systems and Control;Systems and Control