Abstract This paper further investigates the design problem of the functional interval observer for discrete-time systems with disturbances. Two methods are given to design functional interval observers. Given monotone system theory, a Luenberger-like functional interval observer is constructed and sufficient conditions are achieved by Sylvester equations in the first method. The second approach is known as the two-step method. An H∞ functional observer of the system is presented by the H∞ technique, and then the approach of the zonotope is used to estimate its upper and lower boundaries to improve the estimation accuracy. The above methods are applied to two examples for comparison and to show the correctness.

中文翻译：

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具有扰动的离散时间系统的函数区间观测器

摘要 本文进一步研究了具有扰动的离散时间系统的函数区间观测器的设计问题。给出了两种设计函数区间观测器的方法。给定单调系统理论，构造了一个类似 Luenberger 的函数区间观测器，并通过第一种方法中的 Sylvester 方程获得了充分条件。第二种方法称为两步法。用H∞技术给出了系统的H∞函数观测器，然后利用zonotope的方法估计其上下边界以提高估计精度。将上述方法应用到两个例子中，以进行比较并证明其正确性。