In this dissertation, the problem of failure tolerant control is studied to increase the reliability of the computer-controlled industrial control system. The goal of the failure tolerant control system is to retain the stability and performance degradation within allowable degree despite the failures on actuators and/or sensors of the system. To increase the reliability, a hardware redundancy scheme for all components may be a kind of available method but in this case the extra costs, volume, weight and complex maintenance will be more burden than the expected benefits. On the other hand, using an analytic redundancy, which is a software technique, more available failure tolerant control scheme can be obtained. However, since the analytic redundancy is based on the system modeling, the uncertainty problem is inevitable. In this dissertation, a failure tolerant control scheme for the system with unknown inputs is suggested. The unknown inputs are caused by the structured uncertainty and the disturbances. To solve the robust failure tolerant control system design problem, the problem is divided into three subproblems and studied respectively. The first is the unknown input observer design problem(UIOP), which is to design an observer that can estimate the true system state despite any initial value of the state and unknown inputs. The second is the failure diagnosis observer problem(FDOP), which is to design an observer that can estimate the true system state and failures despite any initial state and unknown inputs. For the stochastic systems, when the system is corrupted by the noises, in the designing of the unknown input observer and failure diagnosis observer, the characteristics of the noises should be considered. Thus, like the Kalman-filter, minimum variance observer design procedures for each observers are also studied. The final subproblem is to design a control scheme which can accommodate the failures and unknown inputs and to retain the performance degradation within allowable tolerance(RFAP). Based on the failure diagnosis observer of FDOP, an observer-based failure tolerant control scheme is suggested. The usability of the suggested unknown input observer and failure diagnosis observer in deterministic system and stochastic system are shown via numerical examples respectively. Also, the feasibility of the suggested failure tolerant control scheme is shown via a numerical example.