Identification of Fractional Discrete Linear System Based on Information Compression Matrix

The identification issues of fractional system mainly are how to deal with structure identification and parameters estimation. In this paper, the single input and single output fractional-order linear discrete system with the colored noise is first described. Then, the information compression matrix is constructed by objective functions with different orders, and the decomposition and transformation theorem of the information compression matrix and its proof are given. On this basis, a structure judgment criterion for extracting the optimal model is proposed to simultaneously realize the identification of the model structure, order and parameters of fractional order systems by alternating calculation of information compression matrices. The simulation results demonstrate the effectiveness of the proposed method.