MODEL REDUCTION BASED ON THE GRAPH TOPOLOGY

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1. The continuous relation between models and system performances is discussed. It is shown that system performances depend continuously on the models if the proximity of the plants transfer functions are measured in the graph topology. This result enhances the importance of the graph topology in approximating the plant models.2. It is recognized that the H2-optimal solution is easy to calculate comparing to H* solution. To highlight the superiority of H* solution, the difference of the optimal solutions of H2, and H* control problems is investigated. It is shown that the H* solution approaches H2-solution for all frequencies in the pass band of the waiting function if the cut off characteristics become steep and tend to the ideal ones. This theoretical result says that H2 solution can be used instead of H* solution in some cases.3. It is shown that the stable rational function may be approximated within any prescribed error by a rational function, the poles of which are arbitrarily given in advance. From this result, it is possible to design an H* optimal feedback system whose poles are constrained to locate in a specified stability domain. This result has been published as a full paper.4. Rational approximation of time delays is important from a practical view point. A relationship of error bound and the degree of padeapproximation is derived. This is useful for estimating dimensions of the approximants.5. Model reduction is difficult in the case where the system is stiff, i. e., it contains fast modes and slow modes at the same time. For such situations the time-frequency analysis is relevant to derive a new methodology for the approximation problem. From this motivation, we have treated the approximation problem by using wavelet transforms. This approach will yield fruitful research areas in future.