二阶广义分布参数系统的谱分布

基金项目: 美国国家自然科学基金资助项目(DMS-9406959);陕西省三五人才工程专项基金资助项目(199821)

Spectrum Distribution of the Second Order Generalized Distributed Parameter Systems

1.
Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049, P.R.China;
2.
Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, P.R.China;
3.
Department of Mathematics, Southwest Texas State University, Texas 78666, USA

摘要: 应用泛函分析算子理论的方法研究了Hilbert空间中二阶广义分布参数系统的谱分布问题,利用有界线性算子的广义逆给出了所讨论问题的解及解的构造性表达式。这对研究二阶广义分布参数系统的镇定及渐进稳定性问题都有重要的理论价值。
- 二阶广义分布参数系统 /
- 谱分布 /
- Hilbert空间 /
- 算子的广义逆
Abstract: Spectrum distribution of the second order generalized distributed parameter system was discussed via the functional analysis and operator theory in Hilbert space.The solutions of the problem and the constructive expression of the solutions are given by the generalized inverse one of bounded linear operator.This is theoretically important for studying the stabilization and asymptotic stability of the second order generalized distributed parameter system.
- second order generalized distributed parameter system /
- spectrum distribution /
- Hilbert space /
- generalized inverse one of bounded linear operatiors

[1]	Jóder L,Femandez M L.An implicit difference method for the numerical solution of coupled system of partial differential equations[J]. Appl Math Comput, 1991,46(2): 127-134.
[2]	Lewis F L.A review of 2-D implicit systems[J].Automatica,1992,28(2):345-354.
[3]	Trzaska Z,Marszalek W. Singular distributed parameter systems[J]. IEE Control Theory and Applications, 1993,40 (5): 305-308.
[4]	GE Zhao-qiang. The stabilizability for a class of generalized system[J]. Applied FunctionalAnalysis, 1993,1(1) :56-61.
[5]	岳东,刘永清.广义分布参数系统的变结构控制[J].控制与决策,1996,11(2):278-283.
[6]	高为炳.变结构控制的理论与设计方法[M].北京:科学出版社,1996.
[7]	杨建辉,刘永清.广义分布参数扰动系统滑动模态控制[J].控制与决策,2000,15(2):14.
[8]	GE Zhao-qiang,ZHU Guang-tian,MA Yong-hao. Pole assignment for the first order coupled generalized control system[J] Control Theory and Applications,2000,17(3) :379-383.
[9]	GE Zhao-qiang, MA Yong-hao. Pole assignment of the coupled generalized system[J]. Systems Science,2000,26(3) :5-14.
[10]	葛照强.算子逆问题及其应用[M].西安:陕西科学技术出版社,1993.
[11]	GE Zhao-qiang. On the pole assignment for the generalized system[A]. In: Uchida K Ed. Proceedings of the First Asian Control Conference [C]. Vol 3. Tokyo: Waseda University, 1994,33-35.
[12]	王康宁,吕涛,邹振宇.分布参数控制系统的极点配置问题[J].中国科学,1982,12(2):172-184.