# A Schur complement application

1. Feb 29, 2016

### leenguyen

Hi all,

I have the following BMI (knowing that P, K and $\gamma$ are unknown with appropriate dimensions; the others are known).
[ {\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}} ] < 0

I would like to know if the above inequality are equivalent to the following by using Schur Complement:

[ {\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}} ] < 0

3. The attempt at a solution

Thank you very much in advance for your replies.

Kind regards,
Lee

Last edited by a moderator: Feb 29, 2016
2. Feb 29, 2016

### Staff: Mentor

In future posts, please don't delete the homework template. Its use is required.
What does the above mean?
You've written it using LaTeX as an array, but an array is not a number, so can't be negative, positive, or even zero.

Also, what is BMI?
Same comment here.