A Robust H∞ Filter for Uncertain Continuous-Time Affine Nonlinear Singular Systems

In the present paper, the problem of robust H∞ filtering for continuous-time affine nonlinear singular systems (ANSSs) with norm-bounded uncertainty is studied. Employing Luenberger-like and certainty equivalent structures, and based on the differential game theory, sufficient conditions for the existence of such filters are derived. These conditions are in the form of a generalized Hamilton–Jacobi–Isaacs (GHJI) inequality and the output injection gain of each filter is obtained as a function of the corresponding GHJI inequality solution. Numerical simulations are provided to demonstrate the applicability of the proposed approach. The results show that the adopted method not only perfectly achieves the estimation goals in the presence of model uncertainties but also outperforms some existing results for known (certain) systems.