In some practical problems, for instance in the control of mechanical systems using accelerometers as sensors, it is easier to obtain the state‐derivative signals than the state signals. This paper shows that (i) linear time‐invariant plants given by the state‐space model matrices {A,B,C,D} with output equal to the state‐derivative vector are not observable and can not be stabilizable by using an output feedback if det (A) = 0 and (ii) the rejection of a constant disturbance added to the input of the aforementioned plants, considering det (A) ≠ 0, and a static output feedback controller is not possible. The proposed results can be useful in the analysis and design of control systems with state‐derivative feedback.