Kalman Filtering for Affine Nonlinear Descriptor Systems

In this paper, we consider the Kalman (or $\mathcal{H}_{2}$)-filtering problem for affine nonlinear descriptor systems. Two types of filters are discussed, namely, (i) singular; (ii) normal, and sufficient conditions for the solvability of the problem in terms of Hamilton–Jacobi–Bellman equations (HJBEs) are presented. The results are also specialized to linear systems in which case the HJBEs reduce to a system of linear-matrix-inequalities (LMIs). Examples are also presented to illustrate the results.

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