linear feedback system becomes unstable with high gains

Hello everyone,

I have a linear time-invarient system with a feedback gain, e.g x_dot=-c*A*x for the closed-loop system. I increase the gain c making the eigenvalues further left on the imaginary plane. However, in the matlab simulation, the system becomes unstable when the gain is higher than some value. This is not because some eigenvalues locate on the right half plane. I guess this is because of the numerical errors of the simulation in which I use accumulation for integration. Could anyone provides more insight on this issue and let me know how to solve it? Otherwise, the results of eigenvalue analysis cannot be well validated in time domain.

Many thanks,

Xiao