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A number of necessary and sufficient conditions are derived, which must be satisfied by the plant d.c. gain matrix of a linear time invariant system in order for an integral controller to exist for which the closed loop system is stable. Based on these results, the robustness of integral control systems is analyzed, i.e., the family of plants is defined which are stable when controlled with the same integral controller. Conditions for actuator/sensor failure tolerance of systems with integral control are also given. Finally, parallels are drawn between the results of this paper and the bifurcation theory of nonlinear systems.