论文标题
通过提升和插值的绝对稳定性
Absolute Stability via Lifting and Interpolation
论文作者
论文摘要
我们重新审视了绝对稳定性的经典问题；在反馈中评估给定线性时间不变（LTI）工厂的稳健稳定性，其非线性属于某些给定功能类别。标准结果通常采用LTI工厂的足够条件的形式，其中最不保守的是基于O'Shea-Zames--Falb乘数。我们提出了基于提升和插值的替代分析，该分析直接构建了Lyapunov函数，该功能可以证明绝对稳定性，而无需诉诸频率域的不平等或积分二次约束。特别是，我们使用线性矩阵不等式来搜索lyapunov函数，这些函数在迭代术中是二次的，在升起的空间中系统的相应函数值中的线性搜索。我们表明，我们的方法在一组基准问题上恢复了最先进的结果。
We revisit the classical problem of absolute stability; assessing the robust stability of a given linear time-invariant (LTI) plant in feedback with a nonlinearity belonging to some given function class. Standard results typically take the form of sufficient conditions on the LTI plant, the least conservative of which are based on O'Shea--Zames--Falb multipliers. We present an alternative analysis based on lifting and interpolation that directly constructs a Lyapunov function that certifies absolute stability without resorting to frequency-domain inequalities or integral quadratic constraints. In particular, we use linear matrix inequalities to search over Lyapunov functions that are quadratic in the iterates and linear in the corresponding function values of the system in a lifted space. We show that our approach recovers state-of-the-art results on a set of benchmark problems.
