State-Space System Realization With Input- and Output-Data Correlation

This paper introduces a general version of the information matrix consisting of the autocorrelation and cross-correlationmatrices of the shifted input and output data. Based on the concept of data correlation, a new system realization algorithm was developed to create a model directly from input and output data. The algorithm starts by computing a special type of correlation matrix derived from the information matrix. The special correlation matrix provides information on the system-observability matrix and the state-vector correlation. A system model was then developed from the observability matrix in conjunction with other algebraicmanipulations. This approach leads to several di erent algorithms for computing system matrices for use in representing the system model. The relationship of the new algorithms with other realization algorithms in the time and frequency domains is established with matrix factorization of the information matrix. Several examples are given to illustrate the validity and usefulness of these new algorithms.