Relaxing the Assumptions of Standard H_* Control

H_* 控制是一种给出鲁棒控制系统设计方法的理论。然而，几个相对较强的条件施加在适用的控制问题，如：1。（A，B_2）是可镇定的，（A，C_2）是可检测的，2.G_（s）和G_（s）没有j ω零点，3.D_（s）是列满秩的，D_（s）是行满秩的.为了避免这些条件，本研究得到了以下结果：a.违反第一和第二条件的典型控制问题包括伺服问题，其中引入不稳定加权函数，将内模原理应用到H_* 控制问题的设定中.<12><21><12><21>为了解决这一问题，引入本质稳定的概念和保证控制器具有内模的附加条件，首先解决了H_* 伺服问题。我们的进一步研究甚至解决了这个问题，而不需要假设附加条件。然而，得到的理论的证明是相当复杂的。因此，为了简化证明，我们接下来引入了综合稳定性的概念，并试图通过另一种方法来解决这个问题。B.当输入和输出的放置不平衡时，违反了第二和第三个条件。这包括一个H_* 控制问题，其中真实的植物有极的jomega轴。为了克服这一困难，本文首先引入描述子表示，分析了虚轴上和无穷远处都有零点的对象的谱分解问题。然后，基于该谱分解方法，推导了非标准H_2控制和H_* 控制方案，并通过工业应用验证了H_* 伺服设计方法的有效性。所得理论结果为非标准H * 控制问题的研究奠定了基础。

The H_* control is a theory giving fundamental design method of robust control systems. However, several relatively strong conditions are imposed on applicable control problems such that :1.(A,B_2) is stabilizable and (A,C_2) is detectable.2.G_<12> (s) and G_<21> (s) have no jomega zeros.3.D_<12> is of full column rank and D_<21> is of row full rank.In order to avoid these conditions, the following results are gained in this research.a.Typical control problems violating the first and second conditions include the servo problem, where unstable weighting functions are introduced to implement the internal model principle into the H_* control problem setting. In order to give a solution to this problem, introducing a notion of essential stability and additional condition which guarantees for the controller to have the internal model, we firstly solved the H_* servo problem. Our further investigation even solved the problem without assuming the additional condition. However, the proof of the obtained theory was rather complicated. Therefore, to simplify the proof, we next introduced a notion of comprehensive stability and tried to solve the problem by an alternative procedure.b.The second and third conditions are violated when placement of inputs and outputs is unbalanced. This includes an H_* control problem where real plants have poles on the jomega axis. In order to get around the difficulties, we firstly introduced descriptor representation and analyzed spectral factorization problem for plants having zeros on the imaginary axis as well as at infinity. Then, based on this spectral factorization, we derived nonstandard H_2 control as well as H_* control solutions.Effectiveness of the proposed H_* servo design method was proven by several industrial applications. The theoretical results obtained here give foundation of researches on nonstandard H_* control problems.