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In this paper, the effect of control systems, as a missing (but significant) actor, on the performance of alarm systems is studied. The interplay of control and alarm performance is justified, and it is shown that a state-feedback controller, which is designed to achieve a good quality of control (in terms of minimum output variance), has both desirable and undesirable consequences on the performance of alarm systems. To pave the path for finding a robust controller solution, a new alarm index is introduced and an analytical expression of the performance is derived for signals, known systems, and systems with parameter uncertainties. A set of linear matrix inequalities (LMIs) is proposed for the controller design to satisfy the required control and alarm performance. The effectiveness of the method is illustrated through a case study of a heat exchanger network, which is a frequently used plant in petrochemical industries.