Approximation of cascade connected and feedback structured systems by Mullis-Roberts approximation

A method for constructing a reduced-order model retaining the internal structure of original high-order cascade connected and feedback structured systems is derived by the Mullis-Roberts algorithm. The reduced-order model obtained here is the optimal approximation in the sense that it minimizes the curvilinear integral of the squared norm of an approximation error at the unit circle of the 2-plane. The algorithm for obtaining the reduced-order models is described. One feature of the proposed algorithm is that it is possible to compute reduced-order models of each subsystem independently. The stability of the reduced-order model is not always guaranteed. However, the results of numerical computations show that the reduced-order systems remain stable for almost all randomly selected examples and approximate the input-output behaviour of original systems fairly well.