The problem of designing a constrained feedback control system for a nuclear reactor is investigated. The constraint imposed is that system stability must be retained under possible loss of any arbitrary feedback signal due to failure of the signal sensor. In addition, the control law is synthesized using only partial state availability, and the nominal control system without sensor failure is designed so that the system performs in a desired fashion. Several mathematical models of the reactor dynamics were employed. However, only a model with negative moderator activity coefficients and a single delayed neutron group was used as an example. This model permits a demonstration of two different computational methods for obtaining the required feedback control laws. The first of these two computational methods uses a global procedure for solving polynomial inequalities that represent the stabilization problem. The second method used an algorithm for decreasing a spectral radius function until it is negative, thus allowing implicit control over eigenvalue placement.