LQR error due to round off

I have a cost function which is positive definite, but due to round off errors the computed eigenvalue is slightly negative. The system is fully controllable and observable but the LQR algorithm gets hung up. The R cost function is a 100x100 identity matrix and the Q cost function is an 100 x 100 identity matrix minus a 100 x 100 matrix with all entries equal to 1/100. Any suggestions on how to resolve this issue?

[John Petersen]

Your text is equivalent to

Q = I - .01;

Is this what you mean to do? I don't know your system, but that seems like a strange cost to apply to the states.