Robust Stability Analysis for Feedback Interconnections of Time-Varying Linear Systems
Robust Stability Analysis for Feedback Interconnections of Time-Varying Linear Systems
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DOI：
10.1137/100814676
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发表时间：
2013-01
期刊：
影响因子：
--
通讯作者：
M. Cantoni;U. Jönsson;Sei Zhen Khong
中科院分区：
文献类型：
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作者：
M. Cantoni;U. Jönsson;Sei Zhen Khong
在连续时间环境下研究因果线性系统的反馈关联。发展包括线性时变（LTV）推广Vinnicombe的nu间隙度量和基于积分二次约束的鲁棒L2稳定性定理的不确定反馈互连的潜在开环不稳定系统。这些主要结果是建立在Toeplitz-Wiener-Hopf和Hankel算子以及Fredholm指标的基础上的，对于一类因果线性系统具有以下属性：（i）系统图（即，L2输入-输出对的子空间）允许归一化强右（即，图像）和左（即，核）表示，和（ii）相应的汉克尔算子是紧的。首先验证这些属性的稳定和可检测的LTV状态空间模型，最初激发抽象的制定，随后验证频域乘法不断适当的Callier-Desoer传递函数的分析，确认与时不变理论的发展的一致性。最后，上述鲁棒稳定性定理应用在一个说明性的例子中，关于分布参数系统的反馈互联网络与时变增益。（减）
Feedback interconnections of causal linear systems are studied in a continuous-time setting. The developments include a linear time-varying (LTV) generalization of Vinnicombe's nu-gap metric and an integral-quadratic-constraint-based robust L2-stability theorem for uncertain feedback interconnections of potentially open-loop unstable systems. These main results are established in terms of Toeplitz--Wiener--Hopf and Hankel operators, and the Fredholm index, for a class of causal linear systems with the following attributes: (i) a system graph (i.e., subspace of L2 input-output pairs) admits normalized strong right (i.e., image) and left (i.e., kernel) representations, and (ii) the corresponding Hankel operators are compact. These properties are first verified for stabilizable and detectable LTV state-space models to initially motivate the abstract formulation, and subsequently verified for frequency-domain multiplication by constantly proper Callier--Desoer transfer functions in analysis that confirms consistency of the developments with the time-invariant theory. To conclude, the aforementioned robust stability theorem is applied in an illustrative example concerning the feedback interconnection of distributed-parameter systems over a network with time-varying gains. (Less)