基于ρ-稳定性的无源性定理与小增益定理的推广及其在递推辨识参数自适应算法中的应用
A Generalization of the Passivity Theorem and the Small Gain Theorem Based on $ρ$-Stability, with Application to a Parameter Adaptation Algorithm for Recursive Identification
AI总结：
本文基于ρ-稳定性推广了无源性定理与小增益定理，将其应用于递推辨识参数自适应算法，可解释近期辨识论文的相关结果。
摘要：
常规无源性定理考虑一类闭环系统，其前向通道由严格无源的稳定算子H₁构成，反馈通道由无源算子H₂构成，此时该闭环系统是稳定的。设ρ>1，本文证明当闭环系统的前向通道由严格ρ⁻¹-无源且ρ⁻¹-稳定的算子（该条件弱于上述常规条件）构成，反馈通道由ρ-无源算子（该条件强于上述常规条件）构成时，该闭环系统仍保持稳定。类似地可对小增益定理（增量型或非增量型）进行推广，该方法可解释近期一篇辨识论文中得到的结果。
英文摘要：
The usual passivity theorem considers a closed-loop, the direct chain of which consists of a strictly passive stable operator $H_{1}$, and the feedback chain of which consists of a passive operator $H_{2}$. Then the closed-loop is stable. Let $\rho >1$. We show here that the closed-loop is still stable when the direct chain consists of a strictly $\rho ^{-1}$-passive $% \rho ^{-1}$-stable operator (a weaker condition than above) and the feedback chain consists of a $\rho $-passive operator (a stronger condition than above). Variations on the theme of the small gain theorem (incremental or not) can be made similarly. This approach explains the results obtained in a paper on identification which was recently published.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
