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

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