Nonlinear H∞ observer design for one-sided Lipschitz discrete-time singular systems with time-varying delay

This paper investigates the H-infinity observer design problem for a class of nonlinear discrete-time singular systems with time-varying delays and disturbance inputs. The nonlinear systems can be rectangular and the nonlinearities satisfy the one-sided Lipschitz condition and quadratically inner-bounded condition, which are more general than the traditional Lipschitz condition. By appropriately dealing with these two conditions and applying several important inequalities, a linear matrix inequality-based approach for the nonlinear observer design is proposed. The resulting nonlinear H-infinity observer guarantees asymptotic stability of the estimation error dynamics with a prescribed performance gamma. The synthesis condition of H-infinity observer design for nonlinear discrete-time singular systems without time delays is also presented. The design is first addressed for one-sided Lipschitz discrete-time singular systems. Finally, two numerical examples are given to show the effectiveness of the present approach.