A Schur complement application

[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

The Attempt at a Solution

[/B]
Thank you very much in advance for your replies.

Kind regards,
Lee

 

[Mark44]

In future posts, please don't delete the homework template. Its use is required.

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

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?

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

Same comment here.

The Attempt at a Solution

[/B]
Thank you very much in advance for your replies.

Kind regards,
Lee