This work investigates L2-L∞ filtering problem for a class of stochastic systems with time-delay and randomly occurring phenomena. The purpose of the addressed problem is to design a full order filter to ensure the filtering error system is asymptotically mean-square stable with prescribed L2-L∞ performance. A novel stochastic time-delay system model is established, in which randomly occurring nonlinearities and sensor saturation phenomena are considered. Then, a novel functional containing negative definite terms is constructed to relax the constraints on the functional, and a new free-matrix-based stochastic integral inequality is also given. Meanwhile, a novel L2-L∞ performance analysis method making full use of delay information is proposed. As a result, less conservative conditions for the existence of filters are obtained, under which the L2-L∞ performance level can be achieved for the filtering error system. Numerical examples are employed to show the benefits of the proposed approach.

中文翻译：

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具有随机发生的非线性和传感器饱和的随机延迟系统的 L2-L∞ 滤波

这项工作研究了一类具有时滞和随机发生现象的随机系统的 L2-L∞ 滤波问题。解决问题的目的是设计一个全阶滤波器，以确保滤波误差系统在规定的 L2-L∞ 性能下渐近均方稳定。建立了一种新的随机时滞系统模型，其中考虑了随机发生的非线性和传感器饱和现象。然后，构造了一个新的包含负定项的泛函来放宽对泛函的约束，并给出一个新的基于自由矩阵的随机积分不等式。同时，提出了一种充分利用延迟信息的新型L2-L∞性能分析方法。结果，获得了过滤器存在的不太保守的条件，在此条件下，过滤误差系统可以达到 L2-L∞ 性能水平。数值例子被用来展示所提出的方法的好处。