H∞ filtering for Lipschitz nonlinear singularly perturbed descriptor systems

This paper presents a new framework of H_∞ filter for a class of singularly perturbed descriptor systems (SPDSs) with nonlinear uncertainty satisfying Lipschitz condition. Based on the extensions of the robust stability analysis for SPDSs, we firstly carry out the H_∞ performance and admissibility analysis for the filtering error system, and obtain a sufficient condition for the existence and uniqueness of the solution of the system, in which no small perturbed parameter is involved. Then, by using some elaborate matrix inequality transformation techniques, we successfully remove the nonlinear relationship between the filter parameters and other matrix variables, then a linear matrix inequality based design approach for the proposed H_∞ filter is obtained, which has no numerical stiff problem and is numerically efficient.