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

周期性离散时间系统广义不变子空间与抗扰问题的研究

• 批准号: 13650449
• 负责人: OTSUKA Naohisa
• 金额: $ 1.54万
• 依托单位: Tokyo Denki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13650449/
• 关键词: Periodic System; Invariant Subspaces; Geometric Approach; Disturbance-Rejection Problems

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.

这项研究的项目由以下五个部分组成。（1）第一个研究是为了调查动态补偿器的最小维度，在所谓的几何方法的框架内解决了干扰 - 拒绝问题。（2）第二项研究是为了引入广义不变的子空间的概念，并研究了对局部不确定的局部研究属性的概念。借助线性不确定的周期系统的状态和 /或静态输出反馈，并获得问题的可溶性条件。（4）第四个研究是介绍广义（C（k），A（k），A（k），a（k），b（k）） - 配对并介绍该线性不确定的系统的五分之一研究的属性。该问题的可溶性条件。作为上述研究的结果，引入了不确定的线性周期系统的一些广义不变子空间和广义（C（k），A（k），a（k），b（k））的概念，并研究了它们的性质。此外，制定了不确定线性周期系统的状态反馈，输出反馈和动态补偿器的干扰 - 反馈问题，并分别给出了一些解决性条件。

项目成果

N.Otsuka: "Generalized (C, A, B)-pairs for Linear Discrete-Time Systems"Proc. of the American Control Conference(ACC'02). 2418-2423 (2002)

N.Otsuka：“线性离散时间系统的广义（C，A，B）对”Proc。

N.Otsuka, R.Abdursul: "Further Studies on Generalized Invariant Subspaces"Proc. of the IEEE Region 10 Technical Conference on Computers, Communications, Control and Power Engineering(TENCON'02). 1327-1330 (2002)

N.Otsuka，R.Abdursul：“广义不变子空间的进一步研究”Proc。

N. Otsuka: "Disturbance-Rejection Problems with Low Order Dynamic Compensator for Linear ω-Periodic Discrete- Time Systems"IEEE Transactions on Automatic Control. 46, No.4. 631-635 (2001)

N. Otsuka：“线性 ω 周期离散时间系统的低阶动态补偿器的干扰抑制问题”IEEE 自动控制交易，第 46 期，第 4 期，631-635 (2001)。

N.Otsuka: "Generalized (C_γ(・),A_α(・),B_β(・))-pairs for Linear ω-Periodic Discrete-Time Systems"Transaction of the Society of Instrument and Control Engineers. Vol.39,No.1. 25-34 (2003)

N.Otsuka：“线性 ω 周期离散时间系统的广义（C_γ（·），A_α（·），B_β（·））对”仪器与控制工程师协会学报第 39 卷，第 1 期。 1. 25-34 (2003)

N.Otsuka: "Generalized Controlled and Conditioned Invariances for Linear ω-Periodic Discrete-Time Systems"Linear Algebra and Its Application. Vol.327/1-3. 207-223 (2001)

N.Otsuka：“线性 ω 周期离散时间系统的广义受控和条件不变性”线性代数及其应用，第 327 卷 207-223（2001 年）。