Robust Sliding Window Observer-Based Controller Design for Lipschitz Discrete-Time Systems

Abstract The aim of this paper is to develop a new observer-based stabilization strategy for a class of Lipschitz uncertain systems. This new strategy improves the performances of existing methods and ensures better convergence conditions. The observer and the controller are enriched with sliding windows of measurements and estimated states, respectively. This technique allows to increase the number of decision variables and thus get less restrictive and more general LMI conditions. The established sufficient stability conditions are in the form of Bilinear Matrix Inequality (BMI). The obtained constraint is transformed, through a useful approach, to a more suitable one easily tractable by standard software algorithms. Numerical example is given to illustrate the performances of the proposed approach.