MODEL REDUCTION BASED ON THE GRAPH TOPOLOGY

1.讨论了模型与系统性能之间的连续关系。它示出了系统的性能连续依赖于模型，如果植物的传递函数的接近度在图拓扑结构中测量。这一结果增强了图拓扑在近似对象模型中的重要性.与H* 解相比，H2-最优解更易于计算。为了突出H* 解的优越性，研究了H * 控制问题和H* 控制问题最优解的差异。研究表明，如果截止特性变得陡峭并趋于理想，则对于等待函数通带内的所有频率，H* 解都接近H2解。这一理论结果表明，在某些情况下，可以使用H2溶液代替H* 溶液。它表明，稳定的有理函数可以近似在任何规定的误差由有理函数，其极点是任意给定的。从这个结果，它是可能的，设计一个H* 最优反馈系统的极点被约束位于一个指定的稳定域。这一结果已全文发表。从实用的观点来看，时间延迟的合理近似是重要的。导出了误差界与Pade逼近阶的关系式。这对于估计近似值的维数是有用的。当系统为刚性时，模型降阶是困难的.例如，它同时包含快速模式和慢速模式。对于这种情况下的时间-频率分析是相关的，以获得一个新的方法的近似问题。从这个动机，我们已经处理的近似问题，利用小波变换。这种方法将在未来产生富有成效的研究领域。

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.