高维非线性电阻动态电路惟一稳态研究

冯平

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高维非线性电阻动态电路惟一稳态研究

冯平

文章导航 > 武汉大学学报 ● 信息科学版 > 2002 > 27(2): 212-215

冯平. 高维非线性电阻动态电路惟一稳态研究[J]. 武汉大学学报 ● 信息科学版, 2002, 27(2): 212-215.

引用本文:

冯平. 高维非线性电阻动态电路惟一稳态研究[J]. 武汉大学学报 ● 信息科学版, 2002, 27(2): 212-215.

FENG Ping. The Uniqueness of the Steady State of the Decomposed Dynamic Circuits with Nonlinear Resistors[J]. Geomatics and Information Science of Wuhan University, 2002, 27(2): 212-215.

Citation:

FENG Ping. The Uniqueness of the Steady State of the Decomposed Dynamic Circuits with Nonlinear Resistors[J]. Geomatics and Information Science of Wuhan University, 2002, 27(2): 212-215.

高维非线性电阻动态电路惟一稳态研究

冯平

后勤工程学院电工系, 重庆市长江二路174号, 400016

基金项目: 军队科研基金资助项目(营160号)

详细信息

作者简介:
冯平,讲师,硕士。现主要从事电路理论与应用研究。已在国内外发表论文30多篇。E-mail:fengping@public.cta.cq.cn

中图分类号: TN710

The Uniqueness of the Steady State of the Decomposed Dynamic Circuits with Nonlinear Resistors

FENG Ping

The Electronic and Electrical Research Section, Logistical Engineering University, 174 Changjiang Ⅱ Road, Chongqing China, 400016

摘要: 利用矩阵分解方法,得到了确定具有分解形式的高维含有非线性电阻的动态电路惟一稳态的条件。结果表明,含有非线性电阻的动态电路的惟一稳态,可以用分解矩阵的稳定性决定。
- 非线性电路 /
- 惟一稳态 /
- 矩阵分解
Abstract: The conditions which guarantee the nonlinear nonautonomous circuit to behave as unique steady state are very important and complex.For the nonlinear dynamical circuits with linear resistors,the problems have been solved by previously published papers.But for the network with nonlinear resistors,there have not been satisfactory results to deal with this problem.On the other hand,almost all the known results are not developed particularly for the high degree circuits,So people always find those results very difficult and inconvenient,or even impossible to utilize.The unique steady state of the dynamic circuits with nonlinear resistors in decomposition forms is studied in this paper.The adapted method is the matrix decomposition technique and Liyapunov functions.When handling the large-scale nonlinear circuit,it is very difficult or even impossible to determine its unique steady state directly.Therefore,in this paper,the large-scale circuits are decomposed into several sub-networks with comparatively lower degree,which can be relatively easy to deal with.The stability of each sub-network is determined by Liyapunov functions.And the unique steady state of the nonlinear circuits as a whole is deduce by a Hurwitz matrix,the elements of which are composed of the coefficients related to the stability of the sub networks.The main results obtained in this paper show that the unique steady state of the dynamic circuits with nonlinear resistors in decomposition form can be determined by the stability of some decomposed matrixes.Compared with the known results,the conclusions obtained in this paper make progress at least in the following two aspects.One is that this paper focuses on the nonlinear resistors'functions in the nonlinear circuit and develops an effective method to deal with them,and other is that this paper pays special attention to the handling of the high order circuits,so the results in this paper are very simple and convenient to use,when high order networks considered.From the above,the work in this paper is a great extension of the known results.
- nonlinear circuit /
- steady state /
- matrix decomposition

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高维非线性电阻动态电路惟一稳态研究

冯平

后勤工程学院电工系, 重庆市长江二路174号, 400016

基金项目: 军队科研基金资助项目(营160号)

作者简介:
冯平,讲师,硕士。现主要从事电路理论与应用研究。已在国内外发表论文30多篇。E-mail:fengping@public.cta.cq.cn

收稿日期: 2001-08-10
刊出日期: 2002-02-05

中图分类号: TN710

关键词:

非线性电路 /

惟一稳态 /

矩阵分解

摘要: 利用矩阵分解方法,得到了确定具有分解形式的高维含有非线性电阻的动态电路惟一稳态的条件。结果表明,含有非线性电阻的动态电路的惟一稳态,可以用分解矩阵的稳定性决定。

English Abstract

The Uniqueness of the Steady State of the Decomposed Dynamic Circuits with Nonlinear Resistors

FENG Ping

The Electronic and Electrical Research Section, Logistical Engineering University, 174 Changjiang Ⅱ Road, Chongqing China, 400016

Received Date: 2001-08-10
Publish Date: 2002-02-05

Keywords:

Abstract: The conditions which guarantee the nonlinear nonautonomous circuit to behave as unique steady state are very important and complex.For the nonlinear dynamical circuits with linear resistors,the problems have been solved by previously published papers.But for the network with nonlinear resistors,there have not been satisfactory results to deal with this problem.On the other hand,almost all the known results are not developed particularly for the high degree circuits,So people always find those results very difficult and inconvenient,or even impossible to utilize.The unique steady state of the dynamic circuits with nonlinear resistors in decomposition forms is studied in this paper.The adapted method is the matrix decomposition technique and Liyapunov functions.When handling the large-scale nonlinear circuit,it is very difficult or even impossible to determine its unique steady state directly.Therefore,in this paper,the large-scale circuits are decomposed into several sub-networks with comparatively lower degree,which can be relatively easy to deal with.The stability of each sub-network is determined by Liyapunov functions.And the unique steady state of the nonlinear circuits as a whole is deduce by a Hurwitz matrix,the elements of which are composed of the coefficients related to the stability of the sub networks.The main results obtained in this paper show that the unique steady state of the dynamic circuits with nonlinear resistors in decomposition form can be determined by the stability of some decomposed matrixes.Compared with the known results,the conclusions obtained in this paper make progress at least in the following two aspects.One is that this paper focuses on the nonlinear resistors'functions in the nonlinear circuit and develops an effective method to deal with them,and other is that this paper pays special attention to the handling of the high order circuits,so the results in this paper are very simple and convenient to use,when high order networks considered.From the above,the work in this paper is a great extension of the known results.

冯平. 高维非线性电阻动态电路惟一稳态研究[J]. 武汉大学学报 ● 信息科学版, 2002, 27(2): 212-215.

引用本文:

冯平. 高维非线性电阻动态电路惟一稳态研究[J]. 武汉大学学报 ● 信息科学版, 2002, 27(2): 212-215.

FENG Ping. The Uniqueness of the Steady State of the Decomposed Dynamic Circuits with Nonlinear Resistors[J]. Geomatics and Information Science of Wuhan University, 2002, 27(2): 212-215.

Citation:

FENG Ping. The Uniqueness of the Steady State of the Decomposed Dynamic Circuits with Nonlinear Resistors[J]. Geomatics and Information Science of Wuhan University, 2002, 27(2): 212-215.