Recursive state estimation for noncausal discrete-time descriptor systems under uncertainties

Abstract

This paper describes a method for the online state estimation of systems described by a general class of linear noncausal time-varying difference descriptor equations subject to uncertainties. The method is based on the notions of a linear minimax estimation and an index of causality introduced here for singular difference equations. The online minimax estimator is derived by the application of the dynamical programming and Moore's pseudoinverse theory to the minimax estimation problem. It coincides with Kalman's filter for regular systems. A numerical example of the state estimation for 2D noncasual descriptor system is presented. Keywords: Kalman filtering, online state observer, guaranteed estimation, descriptor systems, singular systems, DAEs.