This paper investigates model matching problem of switched asynchronous sequential machines (ASMs) via semi-tensor product (STP) of matrices. A switched ASM is composed of several input/state ASMs and it cut-overs between submachines in asynchronous mechanism. By using STP method, a switched ASM is depicted as a discrete-time equation form. Under this framework, stable transition matrix and admissible model-input-state transition matrix are defined. Then, two important problems, reachability and optimal control input design of switched ASMs, are discussed by these two new matrices, respectively. Finally, a necessary and sufficient condition for the existence of a controller for model matching is obtained and a practical example on asynchronous error accumulators is provided to show the feasibility of the proposed method.