Conclusion
Contraction theory and applications to nonlinear control systems

Contraction theory is a relevant and powerful tool because it provides modular, robust, and computationally efficient techniques for system analysis and feedback design for a wide variety of control problems. This article focuses on providing an overview of the subject, illustrating the main aspects and properties of contracting nonlinear systems, presenting some results for the design of contracting controllers, and showing how contraction can be applied to relevant control problems.

The theory of contraction for nonlinear dynamic systems is very extensive and constantly evolving. Recently, the vast majority of results on contraction theory have focused on online optimization problems