Abstract
In this paper, we consider the H-infinity-filtering problem for singularly perturbed (two time-scale) nonlinear systems. Two types of filters are discussed, namely, (i) decomposition and (ii) aggregate, and sufficient conditions for the solvability of the problem in terms of Hamilton-Jacobi-Isaac's equations (HJIEs) are presented. Reduced-order filters are also derived in each case, and the results are specialized to linear systems, in which case the HJIEs reduce to a system of linear-matrix-inequalities (LMIs). Based on the linearization of the nonlinear models, upper bounds epsilon* of the singular parameter epsilon that guarantee the asymptotic stability of the nonlinear filters can also be obtained. The mixed H-2/H-infinity-filtering problem is also discussed. Copyright (C) 2010 John Wiley & Sons, Ltd.