## Section: New Results

### Formalization of proofs in control theory

Participants : Damien Rouhling, Cyril Cohen.

We worked on dynamical systems and differential equations. Damien Rouhling fully formalized in Coq LaSalle's invariance principle with the help of Cyril Cohen. This principle uses Lyapunov functions to prove the stability of a dynamical system defined by a differential equation. We wrote a paper about this formalization, which has been published in the proceedings of the ITP 2017 conference [15].

We improved this formalization to apply this principle to an example of robotics and control theory. We formalized in Coq the correctness of a control function for an inverted pendulum. Damien Rouhling wrote a paper about this, accepted for publication at an international conference in early 2018 [20].