A Survey on Semi-Tensor Product of Matrices

被引:0
作者
Daizhan Cheng
Hongsheng Qi
Ancheng Xue
机构
[1] Chinese Academy of Sciences,Institute of Systems Science, Academy of Mathematics and Systems Science
来源
Journal of Systems Science and Complexity | 2007年 / 20卷
关键词
Abstract algebra; differential geometry; dynamic systems; logic; semi-tensor product;
D O I
暂无
中图分类号
学科分类号
摘要
Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. Since then it has been developed and applied to several different fields. In this paper we will first give a brief introduction. Then give a survey on its applications to dynamic systems, to logic, to differential geometry, to abstract algebra, respectively.
引用
收藏
页码:304 / 322
页数:18
相关论文
共 62 条
[1]  
Zhang L.(2005)The general structure of cubic matrices (in Chinese) Sys. Sci. Math. Sci. 25 439-450
[2]  
Cheng D.(1998)On the phase protraits of a class of large nonlinear dynamic systems such as the power systems IEEE Trans. Autom. Contr. 33 4-15
[3]  
Li C.(1988)Stability regions of nonlinear autonomous dynamical systems IEEE Trans. Automat.Contr. 33 16-27
[4]  
Zaborszky J.G.(2004)Quadratic form of stable sub-manifold for power systems Int. J. Robust and Nonlinear Control 14 773-788
[5]  
Huang J.G.(2003)On complexity of power systems J. Sys. Sci. & Complexity 16 391-403
[6]  
Zheng B.(2006)Approximation of the boundary of power system stability region based on semi-tensor theory, Part One: theoretical basis (in Chinese) Auto. Elec. Power Sys. 30 1-5
[7]  
Leung T.C.(2006)Approximation of the boundary of power system stability region based on semi-tensor theory, Part Two: application (in Chinese) Auto. Elec. Power Sys. 30 1-6
[8]  
Chiang H.D.(2004)Non-regular feedback linearization of nonlinear systems via a normal form algorithm Automatica 40 439-447
[9]  
Hirsch M.(2006)Power system transient stability assessment based on quadratic approximation of stability region Electric Power Systems Research 76 709-715
[10]  
Wu F.(1982)Dynamic security regions of power systems IEEE Transactions on Circuits & Systems 29 612-623