Stochastically resilient design of H∞ observers for discrete-time nonlinear systems

A linear matrix inequality based H_infin- type state observer design approach is presented for smooth discrete time nonlinear systems with finite energy disturbances. This observer is designed to maintain disturbance attenuation performance in case of randomly varying perturbations in its gain. A linear matrix inequality is used at each time instant to find the time-varying gain of the observer. Simulation studies are included to explore the performance in comparison to the extended Kalman filter.