AI 中文总结
本文针对离散时间Lurye系统，提出两种数据驱动的稳定性与诱导-ℓ₂性能分析方法，仅需标称系统轨迹数据即可达到基于模型方法的性能，相关条件为凸半定规划且无噪声时可恢复对应模型条件。
AI 中文摘要
本文针对离散时间Lurye系统，开发了用于验证内部稳定性和诱导-ℓ₂性能的数据驱动条件。Lurye系统是标称线性时不变（LTI）系统与静态无记忆非线性环节反馈互联构成的系统，该非线性环节在输入和输出上满足一组已知的二次约束。现有Lurye系统的条件需要标称LTI动态的状态空间实现，而本文的第一个数据驱动结果转而使用标称LTI模块的有限输入、输出和状态轨迹来构建稳定性和性能条件；第二个条件通过确定性子空间辨识技术，从输入输出数据中重构出相似变换下的状态序列，从而无需测量状态轨迹。两种数据驱动条件均表示为凸半定规划，在输入充分激励且无噪声的情况下，可恢复对应的基于模型的Lurye条件。通过一个具有扇区有界非线性环节的简单示例对所提方法进行说明，两种所提方法仅使用标称系统的轨迹数据，即可获得与基于模型方法相同的诱导-ℓ₂增益界。
英文摘要
This paper develops data-driven conditions for certifying internal stability and induced-$\ell_2$ performance of discrete-time Lurye systems. The Lurye system is an interconnection of a nominal LTI system in feedback with a static, memoryless nonlinearity. The nonlinearity satisfies a known set of quadratic constraints on the inputs and outputs. Existing conditions for Lurye systems require a state-space realization of the nominal LTI dynamics. Our first data-driven result instead formulates the stability and performance conditions using finite input, output, and state trajectories of the nominal LTI block. Our second condition removes the need for measured state trajectories by reconstructing the state sequence, up to a similarity transformation, from input/output data. This state reconstruction is performed using deterministic subspace-identification techniques. Both data-driven conditions are expressed as convex semidefinite programs. These conditions, given sufficiently exciting inputs, recover the corresponding model-based Lurye condition in the noiseless setting. The proposed methods are illustrated via a simple example with a sector-bounded nonlinearity. Both proposed methods obtain the same induced-$\ell_2$ gain bound as the model-based approach while using only trajectory data from the nominal system.
