Continuous time double exponential filtering in state space form?
I think I figured it out, dumb mistake in writing the system in continuous time.

$\dot{l} = r_1(u - l)$

$\dot{s} = r_2(\dot{l} - s)$

$\ \ = r_2(r_1(u - l)  + r_1 s - s)$

$\ \ = r_2(r_1(u - l)  + (r_1 - 1)s)$

$\ \ = r_2 r_1(u - l)  + r_2(r_1 - 1)s$

So $$
A = \begin{bmatrix}
-r_1 &amp; 0\\
-r_1r_2 &amp; -r_1r_2\\
\end{bmatrix}
$$

which is stable for all positive $r_1, r_2$!