Robust H∞ observer for nonlinear discrete systems with time delay and parameter uncertainties

The robust H_∞ observer design problem is studied for a class of nonlinear discrete systems with time delay and uncertainties. The nonlinearities are assumed to satisfy global Lipschitz conditions which appear in both the dynamics and the measured output equation. The problem addressed is to design a nonlinear observer such that, for all the admissible uncertainties, the dynamics of the observer error is globally exponentially stable and has a prescribed H_∞ performance. A linear matrix inequality approach is developed and a sufficient condition is obtained to design the nonlinear robust H_∞ observer. Specifically, the convergent rate of the error state can be estimated by the initial condition and time delay of the system. Furthermore, robust H_∞ observer designs for linear (or bilinear) discrete systems with time delay and uncertainties can be obtained directly. Finally, the effectiveness of the proposed observer design is illustrated through two numerical examples.