I have a question about the Schur Complement.

*Is the following inequality*

$\left[ {\begin{array}{*{20}{c}}

{{A^T}P + {K^T}{B^T}P + PA + PBK + C_z^T{C_z}}&{P{B_w}} \\

{B_w^TP}&{ - \gamma }

\end{array}} \right] \prec 0$

*equivalent to*

$\left[ {\begin{array}{*{20}{c}}

{{A^T}P + {K^T}{B^T}P + PA + PBK}&{C_z^T}&{P{B_w}} \\

{{C_z}}&{ - 1}&0 \\

{B_w^TP}&0&{ - \gamma }

\end{array}} \right] \prec 0$

knowing that P,K and $\gamma$ are unknown matrices and scalar with appropriate dimensions. The others are known.

Thank you very much in advance (Happy).

Kind regards,

Lee