Robust H/sub /spl infin// observer for a class of nonlinear discrete systems

In this paper, the robust H/sub /spl infin// observer design problem is studied for a class of nonlinear discrete systems with time-delay and uncertainties. The non-linearities are assumed to satisfy global Lipschitz conditions which appear in both dynamics and 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/sub /spl infin// performance. A linear matrix inequality approach is developed and sufficient condition is obtained to design the nonlinear robust H/sub /spl infin// observer. Specifically, the convergent rate of error state can be estimated by the initial condition and time-delay of the system. Furthermore, robust H/sub /spl infin// 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 a numerical example.