Exponential Decay Rate Conditions for Uncertain Linear Systems Using Integral Quadratic Constraints
Exponential Decay Rate Conditions for Uncertain Linear Systems Using Integral Quadratic Constraints
复制标题
使用积分二次约束的不确定线性系统的指数衰减率条件
DOI：
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发表时间：
2016
影响因子：
6.8
通讯作者：
P. Seiler
中科院分区：
文献类型：
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作者：
Bin Hu;P. Seiler
本技术笔记开发了线性矩阵不等式（LMI）条件，以测试不确定线性系统是否在给定衰减率α下指数稳定。这些新的α-指数稳定性测试是针对由标称线性定常系统和“麻烦”扰动的互连描述的不确定系统导出的。扰动可以包含不确定的参数，时间延迟，或非线性。本技术说明提出了两项关键贡献。首先，证明了不确定LTI系统的α指数稳定性等价于相关尺度系统的（内部）线性稳定性。这使得能够使用积分二次约束（IQCs）从线性稳定性测试导出α指数稳定性测试。这种连接需要IQC被构造为一个缩放的扰动算子。第二个贡献是使用原始扰动的详细结构推导出的标度扰动的IQC列表。最后，所提出的方法和相关工作之间的联系进行了讨论。
This technical note develops linear matrix inequality (LMI) conditions to test whether an uncertain linear system is exponentially stable with a given decay rate α. These new α-exponential stability tests are derived for an uncertain system described by an interconnection of a nominal linear time-invariant system and a “troublesome” perturbation. The perturbation can contain uncertain parameters, time delays, or nonlinearities. This technical note presents two key contributions. First, α-exponential stability of the uncertain LTI system is shown to be equivalent to (internal) linear stability of a related scaled system. This enables derivation of α-exponential stability tests from linear stability tests using integral quadratic constraints (IQCs). This connection requires IQCs to be constructed for a scaled perturbation operator. The second contribution is a list of IQCs derived for the scaled perturbation using the detailed structure of the original perturbation. Finally, connections between the proposed approach and related work are discussed.