Let $M,N \in \mathbb{N}$ and matrices $A\in \mathbb{R}^{M\times N}$, $B\in \mathbb{R}^{M\times M}$, $C\in \mathbb{R}^{N\times N}$. We are interested on the maximal singular value of the matrix \begin{equation} P = \begin{pmatrix} A & B \\ C & D \end{pmatrix} \end{equation} where we can choose the $(N\times M)$ matrix $D$.
Is there a choice of $D$ that minimizes or upper bounds the maximal singular value of the matrix $P$ ?