How to Make a System Contracting via Control
Contraction theory and applications to nonlinear control systems

In this section, we will address the following question: how can we design a controller to make a system contracting via feedback? As with the stabilization of an equilibrium point of a nonlinear system, there is no generic design method that applies to all nonlinear systems. Nevertheless, we have different design approaches for different classes of systems. In what follows, we introduce a few synthesis techniques that stand out for their simplicity. At the end of the section, we will briefly discuss other existing techniques.

Note that in this section, we focus solely on designing a feedback controller such that the system is contracting in a contraction region $\chi$, but we do not address the question of whether such a $\chi$ system is...