On the Tightest Interval-Valued State Estimator for Linear Systems

This paper discusses an interval-valued state estimator for linear dynamic systems. In particular, we derive an expression of the tightest possible interval estimator in the sense that it is the intersection of all interval-valued estimators. This estimator appears, in a general setting, to be an infinite dimensional dynamic system. Therefore practical implementation requires some over-approximations which would yield a good trade-off between computational complexity and tightness.