A Study on Generalized Invariant Subspaces and Disturbance-Rejection Problems for Periodic Discrete-Time Systems

本研究项目由以下五个部分组成。(1)第一项研究是在所谓的几何方法的框架下，研究解决扰动抑制问题的动态补偿器的最小维数。(2)第二个研究是引入广义不变子空间的概念，并研究线性不确定周期系统广义不变子空间的性质。(3)第三部分研究线性不确定周期系统的状态和/或静态输出反馈扰动抑制问题，并得到问题的可解性条件。(4)第四部分是引入广义（C（k），A（k），B（k））-对的概念，研究线性不确定周期系统广义（C（k），A（k），B（k））-对的性质。(5)第五部分研究了不确定线性周期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，引入了不确定线性周期系统的广义不变子空间和广义（C（k），A（k），B（k））-对的概念，并研究了它们的性质。进一步，对不确定线性周期系统分别建立了状态反馈、输出反馈和动态补偿器的扰动抑制问题，并给出了相应的可解性条件。

The project of this study consists of the following five parts.(1) The first study is to investigate about the minimal dimension of dynamic compensator which solves disturbance-rejection problems in the framework of the so-called geometric approach.(2) The second study is to introduce the concepts of the generalized invariant subspaces and to investigate the properties of those subspaces for linear uncertain periodic systems.(3) The third study is to formulate the disturbance-rejection problems with state and / or static output feedback for linear uncertain periodic systems and to obtain the solvability conditions for the problems.(4) The fourth study is to introduce the concepts of generalized (C(k), A(k), B(k))-pair and to investigate the properties of that for linear uncertain periodic systems.(5) The fifth study is to formulate the disturbance-rejection problem with dynamic compensator for linear uncertain periodic systems and to obtain the solvability conditions for the problem.As results of the above studies, some concepts of generalized invariant subspaces and generalized (C(k), A(k), B(k))-pairs for uncertain linear periodic systems were introduced and their properties were investigated. Further, the disturbance-rejection problems with state feedback, output feedback and dynamic compensators for uncertain linear periodic systems were formulated and some solvability conditions were given, respectively.