论文标题
具有单调界限的非线性的乘数
Multipliers for nonlinearities with monotone bounds
论文作者
论文摘要
我们考虑了Lurye（有时是书面的LUR'E）系统，其非线性操作员的特征在于可能是多价非线性，该非线性在单调函数上方和下方界面。可以使用Zames-Falb乘数的子类建立稳定性。结果概括了文献中的类似方法。可以使用凸搜索找到适当的乘数。因为乘数可用于多价非线性，它们可以在循环转换后应用。我们用两个示例说明了新的mutlipliers的力量，一个在连续的时间内，一个在离散的时间内：首先，该方法在文献中表现出优于可用的稳定性测试。在第二个中，我们着重于非对称饱和的特殊情况，对非零稳态外源信号的系统产生了重要的后果。
We consider Lurye (sometimes written Lur'e) systems whose nonlinear operator is characterised by a possibly multivalued nonlinearity that is bounded above and below by monotone functions. Stability can be established using a sub-class of the Zames-Falb multipliers. The result generalises similar approaches in the literature. Appropriate multipliers can be found using convex searches. Because the multipliers can be used for multivalued nonlinearities they can be applied after loop transformation. We illustrate the power of the new mutlipliers with two examples, one in continuous time and one in discrete time: in the first the approach is shown to outperform available stability tests in the literature; in the second we focus on the special case for asymmetric saturation with important consequences for systems with non-zero steady state exogenous signals.
