Interval set‐membership estimation for continuous linear systems

Abstract

SummaryThis 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.