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。结果表明，在图拓扑中测量植物传递函数的接近度时，系统性能连续依赖于模型。这一结果增强了图拓扑在逼近植物模型中的重要性。我们认识到h2 -最优解比H*解更容易计算。为了突出H*解的优越性，研究了H2最优解与H*控制问题的差异。结果表明，当截止特性变得陡峭并趋于理想时，等待函数通带内所有频率的H*解都接近h2解。这一理论结果表明，在某些情况下，H2溶液可以代替H*溶液。证明了稳定有理函数可以用事先任意给定极点的有理函数在规定误差范围内逼近。根据这一结果，可以设计一个H*最优反馈系统，其极点被约束在指定的稳定域中。这一结果已作为一篇全文发表。从实际的角度来看，合理地逼近时滞是很重要的。导出了误差界与平面逼近度的关系。这对于估计近似值的尺寸是有用的。当系统是刚性的，即同时包含快模态和慢模态时，模型化简是困难的。在这种情况下，时频分析可以为逼近问题提供一种新的方法。从这个动机出发，我们用小波变换处理了近似问题。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.