Model reduction for identification of ARX models

In this paper, we discuss the problem of model reduction in ARX system from the point of system identification. When consider the process model represented by the linear regression form, based on the asymptotic analysis results of the unknown parameters vector in the probability frame system, we derive the asymptotic variance matrix form of the unknown parameters vector in ARX system. When obtain the identified parameters vector, we apply the most popular model reduction method L2 method and derive the identification strategy about the unknown parameters vector in the reduced model. Furthermore, we analyse the asymptotic variance matrix form of the unknown parameters vector in the reduced model. Finally, the efficiency and possibility of the proposed strategy can be confirmed by the simulation example results.