An Overview of Integral Quadratic Constraints for Delayed Nonlinear and Parameter-Varying Systems
An Overview of Integral Quadratic Constraints for Delayed Nonlinear and Parameter-Varying Systems
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时滞非线性和参数变化系统的积分二次约束概述
DOI：
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发表时间：
2015
期刊：
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通讯作者：
P. Seiler
中科院分区：
文献类型：
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作者：
H. Pfifer;P. Seiler
提出了一个用于分析非线性和线性参数变化（LPV）时滞系统的稳定性和性能的通用框架。首先，时间延迟算子的输入/输出行为在频域中受到积分二次约束 (IQC) 的限制。恒定延迟是线性、时不变的系统，这导致对这些频域约束的简单、直观的解释。这个简单的解释用于针对恒定延迟和变化延迟导出新的 IQC。其次，非线性和 LPV 延迟系统的性能受到包含 IQC 的耗散不等式的限制。此步骤利用了最新的结果，这些结果表明，在温和的技术条件下，IQC 具有与有限范围时域约束等效的表示。提供了数值示例来证明该方法对于两类系统的有效性。
A general framework is presented for analyzing the stability and performance of nonlinear and linear parameter varying (LPV) time delayed systems. First, the input/output behavior of the time delay operator is bounded in the frequency domain by integral quadratic constraints (IQCs). A constant delay is a linear, time-invariant system and this leads to a simple, intuitive interpretation for these frequency domain constraints. This simple interpretation is used to derive new IQCs for both constant and varying delays. Second, the performance of nonlinear and LPV delayed systems is bounded using dissipation inequalities that incorporate IQCs. This step makes use of recent results that show, under mild technical conditions, that an IQC has an equivalent representation as a finite-horizon time-domain constraint. Numerical examples are provided to demonstrate the effectiveness of the method for both class of systems.