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Summary: In this paper, mixed passive / H∞ hybrid controllers are designed for a delayed Markovian jump system with actuator constraints and alarm signal. The actuator constraints include the unknown actuator bias failure and the actuator partial failure, and the controllers are switched by using alarm signals. First, a sufficient condition for mixed passive / H∞ performance of the closed‐loop system is constructed, and robust controllers and fault‐tolerant controllers are designed, respectively. Then, mixed passive / H∞ observers are presented to ensure that the actuator bias failure is well estimated. Next, an alarm system is proposed by designing multiple thresholds to avoid false alarm, and this system is used to invoke suitable controllers and determine whether to remove the estimated value of actuator bias failure. Finally, two numerical examples are given to illustrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]