A Study on Generalized Invariant Subspaces and Robust Disturbance-Rejection Problems

本研究的方案由以下五个部分组成。(1)第一个研究是引入不确定线性有限维系统的广义不变子空间的概念，并在所谓的几何方法的框架下研究线性系统的特殊有限集与给定的不确定线性系统之间的关系。(2)第二部分研究了广义不变子空间的一些基本性质，并建立了具有输出反馈和动态补偿器的扰动抑制问题。进而得到了问题的可解性条件。(3)第三个研究是引入不确定线性无穷维系统的广义不变子空间的概念，并研究它们的性质。(4)第四部分研究了无穷维系统带状态反馈和输出反馈的扰动抑制问题，并给出了问题的可解性条件。(5)第五部分研究了无限维系统带动态补偿器的扰动抑制问题，得到了该问题的可解性条件，作为上述研究的结果，分别引入了不确定线性有限维和无限维系统的广义不变子空间，并研究了它们的性质，进一步研究了带状态反馈的扰动抑制问题，建立了输出反馈和动态补偿器的数学模型，并给出了可解性条件。

The project of this study consists of the following five parts.(1) The first study is to introduce the concepts of generalized invariant subspaces for uncertain linear finite-dimensional systems and to investigate the relationship between the special finite set of linear systems and a given uncertain linear system in the framework of the so-called geometric approach.(2) The second study is to investigate some fundamental properties concerning the generalized invariant subspaces and to formulate the disturbance-rejection problems with output feedback and / or dynamic compensator. Further, it is to obtain the solvability conditions for the problems.(3) The third study is to introduce the concepts of generalized invariant subspaces for uncertain linear infinite-dimensional systems and to investigate their properties.(4) The fourth study is to formulate the disturbance-rejection problems with state and / or output feedback for infinite-dimensional systems and to obtain the solvability conditions for the problems.(5) The fifth study is to formulate the disturbance-rejection problem with dynamic compensator for infinite-dimensional systems and to obtain the solvability conditions for the problem.As results of the above studies, some generalized invariant subspaces for uncertain linear finite- and/or infinite-dimensional systems were introduced, respectively and their properties were investigated.Further, the disturbance-rejection problems with state feedback, output feedback and dynamic compensator were formulated and some solvability conditions were given.