Abstract This paper investigates the model matching problem of input/output asynchronous sequential machines (ASMs) based on the semi-tensor product (STP) of matrices. The controller of the model matching problem is separated to an observer B and a control unit F . When the controller C = ( F , B ) of the model matching problem exists, the control process is considered with the minimal state set of the controller. Three algorithms which only involve matrix operations are proposed to assign values to the structure matrices of the observer B and the control unit F . In the framework of the STP of matrices, a new algebraic expression for the dynamics of the separated closed-loop system is established and we can easily verify the results of the model matching problem. In this paper, the model matching process is considered with matrix multiplication which is easy to operate. An illustrative example is presented to show the theoretical results and the effectiveness of the proposed algorithms.