Aggregated Reduction Model Based on Partial Block Observability Matrix

For SISO linear system, two aggregated order reduction models are presented by using the partial block-matrix of the observability matrix as aggregation matrix. One is based on minimum norm least squares method and the other is based on generalized inverse of aggregation matrix. When the given system is observable, an approximately observability canonical form reduction model can be obtained and the transfer function of the reduced model approximately equals to that of the original model. When the given system is unobservable, an accurate aggregated reduction model can be obtained and the transfer function of the reduced model exactly equals to the original one. The similarity and difference between these two methods are compared. The model errors are analyzed. These algorithms can be used to improve the accuracy of the reduced models. The reduced model will remain to be stable if the original one is. Simulation results are show to verify the validity and feasibility of the methods.