For the following system

\[\dot{\mathbf{x}}(t)=\mathbf{A x}(t)+\mathbf{B u}(t)\]

the plant matrix \(\mathbf{A}\) is given as

\[\mathbf{A}=\left[\begin{array}{ccc}0 & 1 & 0 \\0 & 0 & 1 \\-6 & -11 & -6\end{array}ight]\]

Find the Transformation Matrix \(\mathbf{P}\), which will transform it to a Diagonal Canonical State-Space model. If the input matrix is

\[\mathbf{B}=\left[\begin{array}{l}0 \\0 \\1\end{array}ight]\]

find the corresponding input matrix for the Diagonal Canonical State-Space model.