数学物理学报(英文版) ›› 1996, Vol. 16 ›› Issue (4): 393-405.

• 论文 • 上一篇    下一篇

CONVERGENCE OF SOLUTIONS FOR RLC-NONLINEAR NETWORKS WITH TIME-VARYING ELEMENTS

蒋断发1, 程正务2   

  1. 1. Dept. of Math., University of Science and Technology of China, Hefei 230026, China;
    2. Electronic Dept., Anhui College of Mechanical and Electrical Engineering, Anhui 241000, China
  • 收稿日期:1994-04-07 修回日期:1994-12-27 出版日期:1996-12-25 发布日期:1996-12-25
  • 基金资助:
    Supported by the National Natural Science Foundation of China.

CONVERGENCE OF SOLUTIONS FOR RLC-NONLINEAR NETWORKS WITH TIME-VARYING ELEMENTS

Jiang Jifa1, Cheng Zhengwu2   

  1. 1. Dept. of Math., University of Science and Technology of China, Hefei 230026, China;
    2. Electronic Dept., Anhui College of Mechanical and Electrical Engineering, Anhui 241000, China
  • Received:1994-04-07 Revised:1994-12-27 Online:1996-12-25 Published:1996-12-25
  • Supported by:
    Supported by the National Natural Science Foundation of China.

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摘要： This paper studies the asymptotic behavior of solutions for nonlinear RLC-networks which have the following form
L(i)(di/dt)=(∂P(i,v,t)/∂i)), C(v)(dv/dt)=-(∂P(i,v,t)/∂v).
The function P(i,v,t),called tile mired potential function,call be used to construct Liapunov functions to prove the convergence of solutions under certain conditions. Under the assumption that every element value involving voltage source is asymptotically constant, we establish four creteria for all solutions of such a system to converge to the set of equilibria of its limiting equations via LaSalle invariant principle.We also present two theorems on the existence of periodic solutions for periodically excited nonlinear circuits.This results generalize those of Brayton and Moser[1,2].

关键词: Nonlinear networks, nonoscillation and oscillation, asymptotic convergence, periodic solutions, LaSalle invariance principle

Abstract: This paper studies the asymptotic behavior of solutions for nonlinear RLC-networks which have the following form
L(i)(di/dt)=(∂P(i,v,t)/∂i)), C(v)(dv/dt)=-(∂P(i,v,t)/∂v).
The function P(i,v,t),called tile mired potential function,call be used to construct Liapunov functions to prove the convergence of solutions under certain conditions. Under the assumption that every element value involving voltage source is asymptotically constant, we establish four creteria for all solutions of such a system to converge to the set of equilibria of its limiting equations via LaSalle invariant principle.We also present two theorems on the existence of periodic solutions for periodically excited nonlinear circuits.This results generalize those of Brayton and Moser[1,2].

Key words: Nonlinear networks, nonoscillation and oscillation, asymptotic convergence, periodic solutions, LaSalle invariance principle

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