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A formal proof of LaSalle's invariance principle

This repository contains a formal proof in Coq of LaSalle's invariance principle.

It requires Coq v8.6, the Mathematical Components library v1.6.1 and the Coquelicot library v3.0.0. It also depends on Daniel Schepler's proof of Zorn's lemma.

It is organised as follows:

  • coquelicotComplements.v: this file extends the Coquelicot library with set-theoretic notations and results on convergence, closed sets and compact sets.

  • lasalle.v: this file contains the actual proof of LaSalle's invariance principle.

  • vect.v: in this file we prove that Mathematical Components' row vectors inherit Coquelicot's topological structures.

  • tychonoff.v: this file contains a proof of Tychonoff's theorem.

  • pendulum.v : in this file we will apply LaSalle's invariance principle to an inverted pendulum.

Authors

Cyril Cohen and Damien Rouhling.