ABSOLUTE STABILITY OF TIME-VARYING NONLINEAR CONTROL SYSTEM

In this paper the authors study two classes of time-varying nonlinear control systems. A few sufficient conditions of absolute stability of these systems were obtained by means of classical analysis and the analogue of the variation of constants formula of nonlinear systems. Moreover, they gave some sufficient conditions of absolute stability in Hurwitz angle for these systems.     

ABSOLUTE STABILITY OF CONTROL SYSTEM WITH MULTI-NONLINEAR FEEDBACK TERMS

ＡＢＳＯＬＵＴＥＳＴＡＢＩＬＩＴＹＯＦＣＯＮＴＲＯＬＳＹＳＴＥＭＷＩＴＨＭＵＬＴＩ－ＮＯＮＬＩＮＥＡＲＦＥＥＤＢＡＣＫＴＥＲＭＳ￥（廖晓昕，王晓君，舒卫华，吴卫华）ＬｉａｏＸｉａｏｘｉｎ；ＷａｎｇＸｉａｏｊｕｎ（Ｄｅｐｔ．ｏｆＭａｔｈｅｍａｔｉｃｓ，...     

Sufficient and necessary conditions for absolute stability of time-delayed Lurie control systems

In this paper, we present some sufficient and necessary conditions for the absolute stability of time-delayed Lurie control systems, which improve the results we obtained before for the absolute stability of direct control, indirect control and critical control of Lurie systems. We also derived certain simple and easy applicable algebraic sufficient conditions for the absolute stability of time-delayed Lurie control systems, which provide a convenient tool for practical control engineers in designing absolutely stable systems or stabilizing nonlinear control systems.     

Aggregation and stability analysis of nonlinear complex systems

The problem of stability of large-scale systems in critical cases is investigated. New form of aggregation for essentially nonlinear complex systems is suggested. With the help of this form the sufficient conditions of asymptotic stability are determined. The results obtained are used for the stability analysis of complex systems by the nonlinear approximation and for the investigation of absolute stability conditions for a certain class of nonlinear systems.     

多非线性控制项的Luré系统绝对稳定的充要条件

本文对具有多非线性控制项的控制系统，得到了绝对稳定的一般性充要条件，并对其特殊情况给出了构造性充要条件．     

Absolute exponential stability of nonlinear systems of differential equations with lag

Constructive sufficient conditions of absolute exponential stability for a class of nonlinear systems of differential equations with lag are found.     

一般Lurie型控制系统的鲁棒绝对稳定性

本文得到一般的Ｌｕｒｉｅ类型非线性控制系统的鲁棒绝对稳定性的充分条件;同时,给出一些例子说明本文结果的有效性．     

具有重叠多非线性项的一般Lurie系统的绝对稳定性

本文研究了具有重叠多非线性项的一般Lurie直接系统的绝对稳定问题.利用关于某个变元绝对稳定的概念,获得了绝对稳定的充要条件和一些充分条件,推广了现有的一些研究结果.     

具有重叠多非线性项的一般Lurie系统的绝对稳定性

本文研究了具有重叠多非线性项的一般Lurie直接系统的绝对稳定问题. 利用关于某个变元绝对稳定的概念, 获得了绝对稳定的充要条件和一些充分条件, 推广了现有的一些研究结果.     

具多个非线性反馈项的一般Lurie控制系统的绝对稳定性

本文研究了具多个非线性反馈项的一般Lurie控制系统的绝对稳定性问题,由Lyapunov函数方法,得出了绝对稳定的新的充分必要条件和一些实用的充分条件,这些条件推广了集合稳定性.一个数值例子说明了本文结果的有效性.     

Absolute stability of general lurie type indirect control systems

1. IntroductionThe absolute stability problem is one of the central topics of the stability theory for itstheoretical and engineering importance. UP to date, this problem has been studied by manyauthors [1--9], and many sufficient conditions and some necessary and sufficiellt conditions inspecial cases for absolute stability are obtained. In papers [7,8], Liao gave a necessary andsufficient condition for absolute stability for partial arguments. In this paperg by using anew concept of absolut…     

Stability of a program manifold of control systems with locally quadratic relations

We establish sufficient conditions for the absolute stability of a program manifold of control systems. In the case where the Jacobi matrix is degenerate, sufficient conditions for the absolute stability of a program manifold is obtained by reduction to the central canonical form.     

具重叠非线性项的一般Lurie系统的绝对稳定性

利用关于变元σ绝对稳定的概念,我们对具重叠非线性项的一般Lurie直接系统得到了绝对稳定的充要条件,并给出一个实用的充分条件.一个数值例子说明了本文结果的有效性.     

一类具有两个非线性控制项的系统绝对稳定的充要性条件

本文给出一类具有两个非线性控制项的系统绝对稳定的充要性判据.该判据关于未定常数均是线性的,易于检验,且有较广适用范围.     

具有多个非线性项的一般Lurie直接控制系统的绝对稳定性

在本文中，依据文［８］提出的关于变元σ绝对稳定的概念，我们对具有多个 非线性项的一般Ｌｕｒｉｅ直接系统得到了绝对稳定的新的充要条件，并给出一些实用的 充分条件．一个数值例子说明了本文结果的有效性．     

离散型Lurie控制系统绝对稳定的充分必要条件

本文研究了离散型Lurie控制系统(1)在非线性函数f(σ)满足f(0)=0,σf(σ)>0(σ≠0)(2)或f(0)=0,0≤k₁≤f(σ)/σ≤k₂<+∞(σ≠0)(3)时,零解的绝对稳定性。给出了系统(1)在满足条件(2)时零解绝对稳定的构造性充要条件,并得到了系统(1)的简化系统在满足条件(3)时,绝对稳定的充分及充要判据。     

Absolute Stability of General Lurie Control Systems with Multi-Nonlinear Feedback Terms

In this paper, the problem of absolute stability for general Lurie control systems with multi-nonlinear feedback terms is investigated. From the Lyapunov function approach, new necessary and sufficient conditions and some practical sufficient conditions of absolute stability are derived, which improve the absolute stability for the set. A numerical example illustrates the effectiveness of the proposed results. The project is supported by the National Natural Science Foundation of China (No. 19871005) and the Foundation of Doctoral Programme of the Educational Ministry of China (No. 1999000722)     

关于变时滞Lur’e间接控制系统的绝对稳定性

本文研究了变时滞Lur’e间接控制系统的绝对稳定性.利用M-矩阵性质及不等式技巧,通过引进可调参数,得到了变时滞Lur’e间接控制系统与时滞相关绝对稳定性新的充分条件.文中的结论推广和改进了已有文献中相应结果.     

一般离散型Lurie控制系统的绝对稳定性

本文给出一类一般离散型Ｌｕｒｉｅ控制系统绝对稳定的充要条件及充分条件     

差分系统平衡点的判别

平衡点在研究差分系统的零解的稳定性时具有极其重要的作用.本文首先给出了线性差分系统平衡点存在的充要条件,然后给出非线性差分系统平衡点存在的充分条件,最后给出了高阶差分系统平衡点存在的充分条件.