Nonlinear Robust Filtering of Sampled-Data Dynamical Systems

This work is concerned with robust filtering of nonlinear sampled-data systems with and without exact discrete-time models. A linear matrix inequality (LMI) based approach is proposed for the design of robust $H{\infty}$ observers for a class of Lipschitz nonlinear systems. Two type of systems are considered, Lipschitz nonlinear discrete-time systems and Lipschitz nonlinear sampled-data systems with Euler approximate discrete-time models. Observer convergence when the exact discrete-time model of the system is available is shown. Then, practical convergence of the proposed observer is proved using the Euler approximate discrete-time model. As an additional feature, maximizing the admissible Lipschitz constant, the solution of the proposed LMI optimization problem guaranties robustness against some nonlinear uncertainty. The robust Hinfty observer synthesis problem is solved for both cases. The maximum disturbance attenuation level is achieved through LMI optimization. At the end, a path to extending the results to higher-order approximate discretizations is provided.