通过积分二次约束进行指数稳定性分析
Exponential Stability Analysis via Integral Quadratic Constraints
AI总结：
本文提出一种通用方法，通过扩展的积分二次约束库，提供更少保守的指数稳定性证书计算方法，通过数值例子验证其有效性。
摘要：
积分二次约束（IQCs）理论允许验证包含非线性或不确定元素的系统稳定性及增益界性质。增益界常暗示指数稳定性，但计算有用的指数衰减率数值界具有挑战性。本文提出了一种扩展经典IQC结果的方法，导致一种可计算的程序，用于找到比仅从$L_2$增益界计算的证书更少保守的指数速率证书。还提供了一个扩展的IQC库以证明指数稳定性，并通过数值例子展示了该技术的有效性。
英文摘要：
The theory of integral quadratic constraints (IQCs) allows verification of stability and gain-bound properties of systems containing nonlinear or uncertain elements. Gain bounds often imply exponential stability, but it can be challenging to compute useful numerical bounds on the exponential decay rate. This work presents a generalization of the classical IQC results of Megretski and Rantzer that leads to a tractable computational procedure for finding exponential rate certificates that are far less conservative than ones computed from $L_2$ gain bounds alone. An expanded library of IQCs for certifying exponential stability is also provided and the effectiveness of the technique is demonstrated via numerical examples.
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