Similar to the Controllability Normal Form we can construct the observability normal form: $$\begin{align*} \dot{\bar{x}}&=\begin{bmatrix}\bar{A}_{11} & 0 \\ \bar{A}_{21} & \bar{A}_{22}\end{bmatrix}\bar{x}(t)+\bar{B}u(t)\\ y(t)&=\begin{bmatrix}\bar{C}_{1} & 0\end{bmatrix}\bar{x}(t) \end{align*}$$with the property that the pair $(\bar{C}_{1},\bar{A}_{11})$ is Observable.