# a schur complement application

#### lepfiev

Dear all,

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