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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 $$A = \begin{bmatrix} -r_1 & 0\\ -r_1r_2 & -r_1r_2\\ \end{bmatrix}$$ which is stable for all ...