This paper investigates robust controllability of switched asynchronous sequential machines (ASMs) with permanent faults. A switched ASM can change its mode through a number of submachines in an asynchronous mechanism. The main objective is to develop a condition for the corrective control scheme that makes the closed-loop system robust against permanent faults while matching its stable-state behavior to that of a reference model. The reachability degradation of the switched ASM caused by faults is described in terms of a matrix expression. In the proposed methodology, each submachine serves as a structural redundancy of the switched ASM allowing robust corrective control of the closed-loop system.