线性离散时变系统的各向异性范数有界实引理
Anisotropic Norm Bounded Real Lemma for Linear Discrete Time Varying Systems
AI总结：
针对输入噪声概率分布不精确已知的有限时域线性离散时变系统，提出各向异性范数有界实引理，通过差分Riccati方程的行列式不等式给出系统各向异性范数不超过给定阈值的状态空间判据。
摘要：
我们考虑一个有限时域线性离散时变系统，其输入是具有不精确已知概率律的随机噪声。统计不确定性由非负参数a描述，该参数约束噪声的各向异性，作为实际噪声分布与具有标量协方差矩阵的高斯白噪声分布的熵理论偏差度量。系统相对于统计不确定随机输入的最坏情况扰动衰减能力由a-各向异性范数量化，该范数是系统的一个适当约束的算子范数。我们建立了一个各向异性范数有界实引理，该引理提供了系统a-各向异性范数不超过给定阈值的状态空间判据。该判据组织为与差分Riccati方程相关的矩阵行列式的不等式，并扩展了H-无穷控制理论中的有界实引理。我们还提供了基于各向异性的鲁棒性能分析的必要背景知识。
英文摘要：
We consider a finite horizon linear discrete time varying system whose input is a random noise with an imprecisely known probability law. The statistical uncertainty is described by a nonnegative parameter a which constrains the anisotropy of the noise as an entropy theoretic measure of deviation of the actual noise distribution from Gaussian white noise laws with scalar covariance matrices. The worst-case disturbance attenuation capabilities of the system with respect to the statistically uncertain random inputs are quantified by the a-anisotropic norm which is an appropriately constrained operator norm of the system. We establish an anisotropic norm bounded real lemma which provides a state-space criterion for the a-anisotropic norm of the system not to exceed a given threshold. The criterion is organized as an inequality on the determinants of matrices associated with a difference Riccati equation and extends the Bounded Real Lemma of the H-infinity-control theory. We also provide a necessary background on the anisotropy-based robust performance analysis.
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