In the previous works, self-repairing control systems (SRCS) have been investigated that can automatically replace failed components with healthy backups so as to maintain stabilities. Fault detection can be exactly accomplished by using a discontinuous detection filter. However, from mathematical viewpoint, existence and uniqueness of the solution of the differential equation expressing the discontinuous SRCS are not assured. In this paper, taking the discontinuity of the detection filter into consideration, based on the Filippov method, the SRCS is modified in order to have a unique Filippov solution and to achieve SRC. In addition, by approximating the discontinuous filter with a continuous one, the continuous SRCS is developed that inherits advantages from the discontinuous SRCS.
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