Extension of H_* and H_* Control Theories with Industrial Applications

H_*控制是目前应用于许多工业控制问题的一种理论。然而，我们经常不能使用标准解决方案，因为需要以下限制性先决条件：（A,B_2）是稳定的，（A,C_2）是可检测的。G_<12> (s)是列满秩的，G_<21> (s)是行满秩的。在本研究工作中，我们首先解决了这些问题，并将结果应用于工业应用，以验证其实用性。我们得到的结果如下：1。当我们解决伺服和估计问题时，我们必须处理一个广义的不稳定对象，它的权值违背了第一个条件。为了解决这些非标准问题，我们首先引入了综合稳定性的概念，并利用这一概念提出了解决非标准问题的扩展H_*和H_2控制。当我们使用H_*控制来解决除众所周知的混合灵敏度问题之外的重要问题时，G_<12> (s)和/或G_<21> (s)有时会违反第二个条件。避免这种情况的控制称为奇异控制。通过发展奇异谱分解，求解了奇异H_*控制。将所得结果应用于矿车的控制和电力系统的频率控制。

The H_* control is a theory which nowadays is applied to many industrial control problems. However, we often cannot use the standard solution because of the following required restrictive pre-conditions :1. (A,B_2) is stabilizable and (A,C_2) is detectable.2. G_<12> (s) is of full column rank and G_<21> (s) is of row full rank for all s including *.In this research work, we firstly solved these problems and applied the outcome to industrial applications in order to confirm the usefulness. The results we have obtained are the following :1. When we solve the servo and estimation problems, we have to deal with a generalized plant having unstable weights which violate the first condition. In order to give solutions to these nonstandard problems, we first introduced a notion of comprehensively stability and proposed extended H_* and H_2 controls using this concept which solve the nonstandard problems.2. When we use the H_* control to solve important problems other than the well known mixed sensitivity problem, G_<12> (s) and/or G_<21> (s) sometimes violate the second condition. The control which avoids this condition is called the singular control. We solved the singular H_* controls by developing singular spectral factorization.3. We applied the obtained results to the control of a mine cart and the frequency control of an electricity power system.