Set-membership filtering of uncertain discrete-time rational systems through Recursive Algebraic Representations and LMIs

This paper is about robust filtering/prediction of nonlinear discrete-time systems with rational dependence on the state or uncertainty vectors. The problem is dealt with in a set-membership context, in that the system initial condition, the uncertainties, as well as the noises affecting the dynamics and the measurements are unknown but bounded. A new recursive approach to the prediction of confidence ellipsoids enclosing the state vector at each sampling time is proposed, based on the reformulation of the system model as a recursive algebraic representation. The solution is expressed as a convex optimization problem under linear matrix inequality (LMI) constraints. The method is assessed on some examples.