数学物理学报(英文版) ›› 2000, Vol. 20 ›› Issue (2): 261-272.

• 论文 • 上一篇    下一篇

ON DETERMINATION OF THE IMPULSIVE SOLUTIONS AND IMPULSIVE PROPERTIES TO LINEAR NON-HOMOGENEOUS MATRIX DIFFERENTIAL EQUATIONS

 谭连生   

  1. Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China
  • 出版日期:2000-04-18 发布日期:2000-04-18

ON DETERMINATION OF THE IMPULSIVE SOLUTIONS AND IMPULSIVE PROPERTIES TO LINEAR NON-HOMOGENEOUS MATRIX DIFFERENTIAL EQUATIONS

 TAN Lian-Sheng   

  1. Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China
  • Online:2000-04-18 Published:2000-04-18

摘要:

This note contains three main results. Firstly, a complete solution of the
Linear Non-Homogeneous Matrix Differential Equations (LNHMDEs) is presented that
takes into account both the non-zero initial conditions of the pseudo state and the non-
zero initial conditions of the input. Secondly, in order to characterise the dynamics of the
LNHMDEs correctly,some important concepts such as the state, slow state (smooth state)
and fast state (impulsive state) are generalized to the LNHMDE case and the solution
of the LNHMDEs is separated into the smooth (slow) response and the fast (implusive)
response. As a third result, a new characterization of the impulsive free initial conditions
of the LNHMDEs is given.

关键词: Linear matrix differential equation, impulsive and smooth solution, impul-
sive free initial conditions, {1}-inverse

Abstract:

This note contains three main results. Firstly, a complete solution of the
Linear Non-Homogeneous Matrix Differential Equations (LNHMDEs) is presented that
takes into account both the non-zero initial conditions of the pseudo state and the non-
zero initial conditions of the input. Secondly, in order to characterise the dynamics of the
LNHMDEs correctly,some important concepts such as the state, slow state (smooth state)
and fast state (impulsive state) are generalized to the LNHMDE case and the solution
of the LNHMDEs is separated into the smooth (slow) response and the fast (implusive)
response. As a third result, a new characterization of the impulsive free initial conditions
of the LNHMDEs is given.

Key words: Linear matrix differential equation, impulsive and smooth solution, impul-
sive free initial conditions, {1}-inverse

中图分类号: 

  • 93B11