3. Stability🔗

We start by introducing the most basic notions of stability and how to use them in Lean. This will include Lyapunov stability and asymptotic stability. We will illustrate how to employ LaSalle's invariance principle to prove asymptotic stability even if the Lyapunov function is not strictly decreasing everywhere.

Throughout this document, we will assume that E is a normed space over ℝ.

1. 3.1. Lyapunov stability
2. 3.2. Asymptotic stability
3. 3.3. Lyapunov functions
4. 3.4. LaSalle's invariance principle
5. 3.5. The exponential contraction flow in 1-d