2019/05/25 by Sei Zhen Khong, Khong, Sei Zhen, Chung‐Yao Kao +1
Engineering · #Adaptive Control of Nonlinear Systems #Control and Stability of Dynamical Systems #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.1905.10600
openalex publication_date 2019/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 trade-offs between passivity surplus and deficit. Converse frequency-weighted small-gain and passivity theorems are also established.