论文标题
h \ h \ infty-timal观察者设计的线性系统，在状态，输出和干扰中延迟
H\infty-Optimal Observer Design for Linear Systems with Delays in States, Outputs and Disturbances
论文作者
论文摘要
本文考虑了在状态，输出和干扰中有多个延迟的线性系统的H \ Infty-tim-Timal估计问题。首先，我们在延迟分化方程（DDE）框架中制定了H \ Infty-Aftim-Tim-Timal估计问题。接下来，我们构建了最佳估计器设计框架的等效部分积分方程（PIE）表示。然后，我们表明，在PIE框架中，H \ Infty-Aftimal估计量合成问题可以作为线性PI不等式（LPI）提出。 LPI是LMI对部分积分（PI）运算符代数的概括，可以使用Pietools工具箱解决。最后，我们将最佳估计器的PIE表示为ODE-PDE表示形式 - 一种类似于DDE的形式，但对无限维态估计（时间历史）进行了校正。数值示例表明，我们提出的合成条件会产生具有可证明的h \ infty-goain结合的估计器，与使用基于pade的离散化获得的结果相比，该估计值准确至4个小数位。
This paper considers the H\infty-optimal estimation problem for linear systems with multiple delays in states, output, and disturbances. First, we formulate the H\infty-optimal estimation problem in the Delay-Differential Equation (DDE) framework. Next, we construct an equivalent Partial Integral Equation (PIE) representation of the optimal estimator design framework. We then show that in the PIE framework, the H\infty-optimal estimator synthesis problem can be posed as a Linear PI Inequality (LPI). LPIs are a generalization of LMIs to the algebra of Partial Integral (PI) operators and can be solved using the PIETOOLS toolbox. Finally, we convert the PIE representation of the optimal estimator back into an ODE-PDE representation - a form similar to a DDE, but with corrections to estimates of the infinite-dimensional state (the time-history). Numerical examples show that the synthesis condition we propose produces an estimator with provable H\infty-gain bound which is accurate to 4 decimal places when compared with results obtained using Pade-based discretization.
