Abstract—We study stability conditions for a control system over a linear one-side bounded heat transfer object with the so-called “Schipanov controller”; this controller under perfect imple- mentation must ensure invariant behavior of the object’s output related to the input influence. We study the behavior of the output of a closed system under such possible imperfections in controller implementation as pure delay and inertia; we find classes of influences with respect to which one can ensure stability of the closed system, and find estimates of its output’s response levels to influences from these classes.