Zonotopes and Kalman observers: Gain optimality under distinct uncertainty paradigms and robust convergence

State bounding observation based on zonotopes is the subject of this paper. Dealing with zonotopes is motivated by set operations resulting in simple matrix calculations with regard to the often huge number of facets and vertices of the equivalent polytopes. Discrete-time LTV/LPV systems with state and measurement uncertainties are considered. Based on a new zonotope size criterion called FW-radius, and by merging optimal and robust observer gain designs, a Zonotopic Kalman Filter (ZKF) is proposed with a proof of robust convergence. The notion of covariation is introduced and results in an explicit bridge between the zonotopic set-membership and the stochastic paradigms for Kalman Filtering. No intersection is used and the influence of the reduction operator limiting to a tunable maximum the size of the matrices involved in the zonotopic set computations is fully taken into account in the LMI-based robust stability analysis. A numerical example illustrates the effectiveness of the proposed ZKF.