Hα filtering for discrete-time affine non-linear descriptor systems

In this study, the authors consider the H_∞-filtering problem for discrete-time affine non-linear 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 disrete-time Hamilton-Jacobi-Isaacs equations (DHJIEs) are presented. The results are also specialised to linear systems, in which case the DHJIEs reduce to a system of linear-matrix-inequalities (LMIs). Examples are also presented to illustrate the results.