This article proposes a mixed interval set‐membership estimation (ISME) method for continuous linear time‐invariant (LTI) systems by combining the positive system theory and the set theory. The proposed ISME method gives a new mixed interval‐set estimation framework for continuous LTI systems, whose benefit consists in that it has potential to achieve a balance of computational complexity and robust state estimation conservatism with respect to the interval observer (IO) and the set‐valued observer (SVO) for continuous LTI systems. Particularly, the proposed ISME method first uses a coordinate transformation such that the original system is transformed into an equivalent system. Second, the equivalent system is partitioned into two subsystems, where the first subsystem has a Meztler and Hurwitz subsystem matrix and then an IO is designed for the first subsystem based on the positive system theory. Because it is not guaranteed that the second subsystem also has a Meztler and Hurwitz subsystem matrix, a zonotopic SVO is further designed for the second subsystem based on the set theory. Consequently, an integration of the two steps above provides the whole SE results for the original system. At the end of this article, an example is used to illustrate the effectiveness of the proposed ISME method.

中文翻译：

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连续线性系统的区间集成员估计

本文结合正系统理论和集合理论，为连续线性时不变（LTI）系统提出了一种混合区间集合成员估计（ISME）方法。所提出的ISME方法为连续LTI系统提供了一个新的混合间隔集估计框架，其优点在于，相对于间隔观察者（IO）和集合，它有可能实现计算复杂性和鲁棒的状态估计保守性之间的平衡连续LTI系统的有价值的观察者（SVO）。特别地，所提出的ISME方法首先使用坐标变换，以便将原始系统变换为等效系统。其次，等效系统分为两个子系统，其中第一个子系统具有Meztler和Hurwitz子系统矩阵，然后根据肯定系统理论为第一个子系统设计IO。由于不能保证第二子系统也具有Meztler和Hurwitz子系统矩阵，因此基于集合论为第二子系统进一步设计了局部局部SVO。因此，以上两个步骤的集成为原始系统提供了完整的SE结果。在本文的结尾，使用一个示例来说明所提出的ISME方法的有效性。上面两个步骤的集成提供了原始系统的完整SE结果。在本文的结尾，使用一个示例来说明所提出的ISME方法的有效性。上面两个步骤的集成提供了原始系统的完整SE结果。在本文的结尾，使用一个示例来说明所提出的ISME方法的有效性。