This paper presents the problem of controlling asynchronous sequential machines in the presence of input disturbances, which may be also regarded as an adversary in a game theoretic setting. The main objective is to provide necessary and sufficient condition for the existence of a corrective controller that solves model matching problem of an asynchronous machine suffering from input disturbance. The existence condition can be stated in terms of a simple comparison of two skeleton matrices. The proposed controller eliminates the adversarial effect of input disturbance and makes the controlled machine mimic the behavior of a model in stable-state way. Whenever controller exists, algorithms for their design are outlined and demonstrated in a case study.