$\mathcal{L}_2$状态估计在偶发测量中的保证收敛速度
$\mathcal{L}_2$ State Estimation with Guaranteed Convergence Speed in the Presence of Sporadic Measurements
AI总结：
本文研究了在偶发可用测量和外部扰动存在下，对线性时不变系统状态的估计问题，提出了一种带有连续插值项的观测器，并通过线性动力系统设计，使估计误差在给定衰减率下实现全局指数稳定性，同时考虑了对外部扰动的鲁棒性和$\mathcal{L}_2$-外部稳定性，最后通过三个例子验证了方法的有效性。
摘要：
本文研究了在偶发可用测量和外部扰动存在下，对线性时不变系统状态的估计问题。提出了一种带有连续插值项的观测器，其中插值项由一个线性动力系统提供，其状态在每个采样时间被重置为测量输出估计误差。所得到的系统通过定时触发新测量的到来，并在混合系统框架下进行分析。观测器的设计旨在实现全局指数稳定性，使估计误差集内的值为零。考虑了对外部扰动的鲁棒性和从植物扰动到给定性能输出的$\mathcal{L}_2$-外部稳定性。此外，提出了基于线性矩阵不等式求解的计算高效算法来设计观测器。最后，通过三个例子展示了所提出方法的有效性。
英文摘要：
This paper deals with the problem of estimating the state of a linear time-invariant system in the presence of sporadically available measurements and external perturbations. An observer with a continuous intersample injection term is proposed. Such an intersample injection is provided by a linear dynamical system, whose state is reset to the measured output estimation error at each sampling time. The resulting system is augmented with a timer triggering the arrival of a new measurement and analyzed in a hybrid system framework. The design of the observer is performed to achieve global exponential stability with a given decay rate to a set wherein the estimation error is equal to zero. Robustness with respect to external perturbations and $\mathcal{L}_2$-external stability from the plant perturbation to a given performance output are considered. Moreover, computationally efficient algorithms based on the solution to linear matrix inequalities are proposed to design the observer. Finally, the effectiveness of the proposed methodology is shown in three examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
