ℋ∞ Sliding Window Observer Design for Lipschitz Discrete-Time Systems

This paper focuses on the ℋ∞ observer design for Lipschitz discrete-time nonlinear systems. The main idea consists in using previous measurements in a Luenberger observer through a sliding window to obtain less restrictive constraint. Reformulations of both Lipschitz property and Young’s relation are used to offer greater degree of freedom to the obtained constraint. The presented result is in the form of BMI (Bilinear Matrix Inequality) which is transformed into LMI (Linear Matrix Inequality) through an interesting approach. The resulting constraint can be easily achieved with standard software algorithms. Then, to prove the superiority of the proposed design methodology, a comparison with the classical case is presented. Numerical examples are given to illustrate the effectiveness and the high performances of the proposed filter.