Global Asymptotic Stability

Resources: page=16 - Theorem 4.2

---

[!Theorem 4.2] Let $x=0$ be an equilibrium point for $\dot{x}=f(x)$. Let $V:R^n\to R$ be a continously differentiable function s.t

V(0)=0 ; \text{and} ; V(x)>0, ; \forall , x\neq 0 \ ||x|| \to \infty \implies V(x) \to \infty \ \dot{V}(x)<0, ; \forall , x\neq 0 \end{align}$$

Then $x=0$ is globally asymptotically stable

Radially Unbounded