How can I find P2 in the following inequality?
$$S_{ai} = Q + G P_2 G'- P_2 - \bar{\gamma}^2 G P_2 C' R^{-1} C P_2 G' \prec 0$$
where $R = \beta C P_2 C'+ V$, $\beta=0.9$, $\bar{\gamma} = 0.9$ and
G =
0.5437 0.0768
0.2040 -1.1470
C =
1 0
0 1
Q =
0.1363 0.1527
0.1527 2.9000
Please help me. I think it is not solvable by LMI. please help me if there is any solution for solving this inequality in your idea.