北京大学学报(自然科学版)

一类非线性反馈系统的稳定性分析

喻学刚,黄琳   

  1. 北京大学力学与工程科学系,北京,100871
  • 收稿日期:2000-03-20 出版日期:2001-01-20 发布日期:2001-01-20

Stability Analysis for a Class of Nonlinear Feedback System

YU Xuegang, HUANG Lin   

  1. Dept. of Mechanics & Engineering Science, Peking University, Beijing, 100871
  • Received:2000-03-20 Online:2001-01-20 Published:2001-01-20

摘要: 利用新近发展起来的积分二次约束(IQC)方法,研究了一类较为普遍的非线性反馈连接的 L2-稳定性问题,给出了其稳性分析准则和一些必要条件,这些结果适用于时不变与时变系统。其次,利用已有的结果,研究了非线性环节具有扇区特性的稳定性问题。在单输入单输出(SISO)的情况下,给出了时变系统的圆判据。而在多输入多输出MIMO的情况下,也给出了一个稳定性判据,该结果不要求其非线性环节具有解藕条件。

关键词: 积分二次约束(IQC), 非线性, 适定性, 稳定性

Abstract: Using the integral quadratic constraints (IQC's) methods, the L2-stability for a class of nonlinear feedback system is studied in this paper. Thus some sufficient and necessary conditions are given. These results are suitable for both time-invariant and time-varying systems. As an application, the general time-varying Lur'e problem is studied too. Then the time-varying circle criterion in the SISO case is given. At the same time, in the MIMO case, a stability criterion is given, which doesn't need the decoupling conditions.

Key words: Integral quadratic constraint(IQC), nonlinearity, well-posedness, stability

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