A real-time control system, composed of the controlled processor and the controller computer(s), may have a variety of task types, some of which have tight timing-constraints in generating the correct control input. The maximum period of those task failures tolerable by the system is called the hard deadline, which depends on not only fault characteristics but also task characteristics. In the paper, we extend a method deriving the hard deadline in LTI system executing single task. An algorithm to combine the deadlines of all the elementary tasks in the same operation-mode is proposed to derive the hard deadline of the entire system. For the end, we modify the state equation for the task to capture the effects of task failures (delays in producing correct values) and inter-correlation. We also classify the type of executing the tasks according to operation modes associated with relative importance of correlated levels among tasks, into series, parallel, and cascade modes. Some examples are presented to demonstrate the effectiveness of the proposed methods.