Theoretical Relationship of Set-Based Robust State Estimators: An Optimality Perspective

This article establishes a mathematical framework for discrete-time linear time-invariant systems to compare the optimal state estimation performance of the set-membership estimator, set-valued observer, and interval observer in the polytopic representation. First, the ability of observer gains in reducing the conservatism of state estimation sets is characterized by the support function. Second, the optimal estimation results given by the set-valued and interval observers are derived rigorously. Third, two novel observer gain design methods are proposed for the set-valued and interval observers to achieve their optimal estimation. At the end of this article, intense numerical experiments are conducted to verify the presented analysis results.