$\mathcal{H}_{2}$ Filtering for Discrete-Time Affine Nonlinear Descriptor Systems

Abstract

In this paper, we consider the Kalman (or H 2 )-filtering problem for discrete-time affine nonlinear descriptor systems. Two types of filter are discussed, namely, (i) singular; and (ii) normal. Sufficient conditions for the solvability of the problem in terms of discrete-time Hamilton-Jacobi-Bellman equations (DHJBEs) are presented. The results are also specialized to linear systems in which case the DHJBEs reduce to a system of linear matrix-inequalities (LMIs). Examples are also presented to illustrate the results.