Solving Riccati-like matrix inequality

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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.