Attractive ellipsoid design for robust sliding‐mode observation error in stochastic nonlinear discrete‐time systems

In this paper the observation process of stochastic discrete‐time nonlinear system is analyzed. The system to be observed is assumed to be uncertain, but fulfilling the global "quasi‐Lipschitz" condition and is subjected to stochastic input and output disturbances of a white noise type. The combination of a traditional Luenberger residual term with a discontinuous one is considered. The designing of the best observer gain matrices is realized by using the Robust Attractive Ellipsoid Method for the analysis of the averaged observation error. The construction of this attractive ellipsoid is based on the numerical solution of some matrix optimization problem under specific constraints of Bilinear and Linear Matrix Inequalities (BMI's and LMI's) type applied to improve the attractiveness zone estimation. Two numerical xamples illustrate the effectiveness of the suggested approach.