This paper investigates functional interval estimation for continuous-time linear systems subject to both time-varying and time-invariant uncertainties. Two novel methods are proposed based on peak-to-peak functional observer design and interval analysis. First, we present a splitting-based method that splits the estimation error dynamics into two subsystems to handle the time-invariant disturbances and provide accurate estimation results. Then, to further enhance the estimation accuracy, we present an augmentation-based method that considers the time invariance in both functional observer design and reliable interval estimation. The relationship between a state-of-art method and the proposed methods are analysed theoretically. Finally, simulation results are provided to demonstrate the performances of the proposed methods.

中文翻译：

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具有时不变不确定性的连续时间线性系统的函数区间估计


本文研究了受时变和时不变不确定性影响的连续时间线性系统的函数区间估计。提出了两种基于峰-峰泛函观测器设计和区间分析的新方法。首先，我们提出了一种基于分裂的方法，该方法将估计误差动力学分为两个子系统，以处理时不变的干扰并提供准确的估计结果。然后，为了进一步提高估计的准确性，我们提出了一种基于增强的方法，该方法在函数观察者设计和可靠的区间估计中都考虑了时间不变性。从理论上分析了最先进的方法和所提出的方法之间的关系。最后，给出了仿真结果，验证了所提方法的性能。