Often it is desirable to stabilize a system around an optimal state. This can be effectively accomplished using feedback control, where the system deviation from the desired state is measured in order to determine the magnitude of the restoring force to be applied. Contrary to conventional wisdom, i.e. that a more precise measurement is expected to improve the system stability, here we demonstrate that a certain degree of measurement error can improve the system stability. We exemplify the implications of this finding with numerical examples drawn from various fields, such as the operation of a temperature controller, the confinement of a microscopic particle, the localization of a target by a microswimmer, and the control of a population.