A set of sensing coils to measure plasma position is described. The possibility of placing these coils outside a vacuum vessel (as a resistive shell) is considered by analyzing a feedback system for controlling otherwise unstable axisymmetric motion. A simple model was used to study the axisymmetric stability of a noncircular plasma surrounded by a conducting vacuum vessel and a feedback control system. Suitable choice of the various constants allowed a study of either horizontally or vertically unstable motion, either with or without an iron core and with various configurations for the vacuum vessel. Analytic expressions for the stability limits are derived, together with the specific response to a requested step displacement, giving the overshoot, steady-state error, decay times, and maximum power supply voltage. By suitably choosing an effective decay index both vertical and horizontal motion were studied. The results are applied to TEXT Upgrade (horizontal elongated, with iron core, horizontal unstable) using an effective decay index of -1. >