Recursive state estimation for linear non-causal descriptor systems with uncertain parameters

This paper describes a state estimation approach for a uncertain dynamical system described by linear operator equation in Hilbert space. The uncertainty is supposed to admit a set-membership description. The approach is based on the notion of linear minimax a posteriori estimation. We introduce a new notion of minimax directional observability. It is used to derive the new equations describing the dynamics of the minimax recursive estimator for discrete-time non-causal DAEs in the time domain. The algorithm has the same structure as celebrated Kalman filter if the plant equation is causal. We illustrate the benefits of non-causality of the plant applying our approach to scalar nonlinear set-membership state estimation problem.