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In this report, we study tolerance of semantic faults, one of the crucial issues in the Simplex TM architecture. In particular, we examine semantic faults that cause the controlled device to be unsafe (i.e., unable to carry out its normal operation) and eventually cause the device to become damaged. We also consider fault detection as a safety check. For the class of control systems operating around an equilibrium, the objective of maintaining the safety of the controlled device is formulated as a stabilization problem, and the safety of the controlled device is tested against the stability region of the device under the safety control. To establish the stability region, we apply the Lyapunov stability theory and linear matrix inequality (LMI) methodologies. It is shown that the stability region for a given safety controller as well as a safety control law can be systematically derived by LMI-based approaches. We conclude the report with a summary of the procedure for deriving the safety check and safety controller for a given application. TM Simplex is a trademark of Carnegie Mellon University.