Feedback stabilization of the thermal runaway by compression-decompression is studied by using a one-dimensional transport model that includes the effect of plasma profiles. The stability conditions required for the control system are derived from an eigenvalue analysis. The dynamic responses of plasma parameters to the control are also studied numerically by time integrating the transport equation with locally perturbed initial conditions. The stability conditions on the feedback control system are similar to previous results obtained from the zero-dimensional analysis. Time-dependent analysis shows that thermal runaway initiated by the local disturbances of temperature is suppressed, allowing a stationary burn of the space-dependent plasma.