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This paper deals with the problem of reducing the order of periodic linear timeinvariant control systems which are described by input-output data with no noise. One goal of the procedure given in this paper is to derive from input-output data the frequency transfer function matrix of the model by expanding it to the finite Kautz orthonormal function system. The other is to compose a completely controllable and observable model of the transfer function matrix by using the Gilbert's realization method. The order of expansion and the model dimension have a simple relation depending on the data, where they are identical in the case of a single input and/or a single output. A uniform approximation criterion being is introduced, the relation between the dimension of the reduced model and the error between model and system is made definite. As a practical example a dog systemic circulation is reduced to a two-dimensional model by the method above. This example will be useful in designing the adaptive control system of the cardiac assist pump being developed by the authors.

Reduction Method of Periodic Control Systems by Kautz Orthonormal Function System and Its Application to Systemic Circulation