Converse Theorems for Integral Quadratic Constraints
Converse Theorems for Integral Quadratic Constraints
复制标题
积分二次约束的逆定理
DOI：
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发表时间：
2019
影响因子：
6.8
通讯作者：
Chung
中科院分区：
文献类型：
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作者：
Sei Zhen Khong;Chung
对线性定常系统建立了积分二次约束的匡威定理。证明了当一个与任意满足IQC的系统反馈关联的系统是稳定的时，该系统必然满足互补IQC。这些定理被专门用来导出匡威无源性结果的多个版本。它们涵盖了严格被动性的标准概念以及被动性指标，这些指标表征了被动性盈余和赤字之间的权衡。建立了匡威频率加权小增益和无源性定理。
A collection of converse theorems for integral quadratic constraints (IQCs) is established for linear time-invariant systems. It is demonstrated that when a system interconnected in feedback with an arbitrary system satisfying an IQC is stable, then the given system must necessarily satisfy the complementary IQC. These theorems are specialized to derive multiple versions of converse passivity results. They cover standard notions of strict passivity as well as passivity indices that characterize the tradeoffs between passivity surplus and deficit. Converse frequency-weighted small-gain and passivity theorems are also established.