I have to solve an algebraic Riccati equation but the care command of MATLAB is responding as "Unable to solve the specified Riccati equation because the Hamiltonian spectrum is too close to the imaginary axis."
The equation is $$FX+XF'-XCC'X+Q=0$$ and I am using $$[X,L,G] = care(F',C,Q)$$ in MATLAB.
In my case, the matrices $F, C$ and $Q$ are $$F=\left[\begin{array}{ccc} 0.0162 & -0.0772 & 0.0647 & -0.0207\\ 1.5229 & -4.4023 & 3.7508 & -1.7837 \\ 0.8827 & -2.5508 & 2.1785 & -1.0429 \end{array}\right] \times 10^{3}$$
$$C=\left[\begin{array}{ccc} -0.0000+0.4623i & 4.7301-0.0166i & -0.0000+0.6308i \\ -2.2361-1.5559i & -15.9189-21.5102i & -0.0000-2.1231i \\ 0.0000-0.5416i & -5.5406+0.0170i & 0.0000-0.7390i\end{array}\right] $$
$$Q=\left[\begin{array}{ccc} -0.0003 & -0.0180 & -0.0103 & -0.0032\\ -0.0180 & -1.0347 & -0.6010 & -0.1885 \\ -0.0103 & -0.6010 & -0.3478 & -0.1091 \\ -0.0032 & -0.1885 & -0.1091 & -0.0342 \end{array}\right] \times 10^{5}.$$