Lyapunov norm

Sarah · **Posted:** Sat, 16 Feb 2008 13:07:50 UTC

I want to find the Lyapunov norm for the linear system $\dot x=Ax,x\in\mathbb{R}^2$ with $A= \left( \begin{array}{cc} -\frac{1}{5}&1\\ 0&-\frac{1}{5} \end{array} \right)$
I just learned what the Lyapunov form is, but I thought I could diagonalize the matrix but it's not diagonalizable, so how do I do this?

Lyapunov norm $||\cdot||_2$

$||e^{tA}x||_2\leq e^{-\alpha t}||x||_2, \ \ \ t>0$

for some $\alpha>0$