$K>0\in \mathbb{R}^{n\times n}$, $P>0 \in \mathbb{R}^{n\times n}$ are diagonal positive definite matrices. And $R\geq 0\in \mathbb{R}^{m\times m}$ is positive semi-definite matrix. Let $B\in \mathbb{R}^{n\times m}$, $n>m$ . Let $A\mathbb{R}^{n\times n}$ be a rank-deficient matrix.

I am trying to find the conditions on $K$ (existance) such that, the matrix
\begin{eqnarray}
\begin{bmatrix}
K-P+B R B^\top & KA\\
A^\top K &A^\top K A
\end{bmatrix}\geq 0
\end{eqnarray}.