Given the following inequality
\begin{align} & \gamma \left( Q - (A Q + BY)^T Q^{-1} (A Q + BY) \right) - Y^T R^{1 \over 2} R^{1\over 2} Y - Q Q_1^{1\over2} Q_1^{1\over2} Q \succeq 0 \tag{1} \end{align}
where $\gamma > 0$ is a scalar, $Q \succ 0$, $R \succ 0$ and $Q_1 \succ 0$ are symmetric matrices. The notation $G \succ 0$ denotes that $G$ is positive definite and $G \succeq 0$ denotes that $G$ is positive semidefinite .
How do I convert it to the following form by applying Schur complement?
\begin{align} \begin{bmatrix} Q & (A Q + BY)^T & Q Q_1^{1\over2} & Y^T R^{1 \over 2}\\ (A Q + BY) & Q & 0 & 0 \\ Q_1^{1\over2} Q & 0 & \gamma I & 0 \\ R^{1\over 2} Y & 0 & 0 & \gamma I \end{bmatrix} \succeq 0 \tag{2} \end{align}
I understand \begin{align} \begin{bmatrix} E & F \\ F^T & G \end{bmatrix} \succeq 0 \tag{3} \end{align}
is equivalent to the inequalities:
\begin{align} G \succ 0,\qquad E - F G^{-1} F^T \succ 0 \tag{4} \end{align}
or equivalently,
\begin{align} E \succ 0,\qquad G - F^T E^{-1} F \succ 0 \tag{5} \end{align}
How do I extend the core ideas from inequalities $(3)$-$(5)$ to inequalities $(1)$ and $(2)$?
I want to understand how to arrive at a form like (2) from (1) for the purpose of constructing LMI problems in control theory. This example is from the proof of theorem 1 in the Robust Constrained Model Predictive Control using Linear Matrix Inequalities [PDF]. Is there a general method or technique to get to (2) from (1)?