# Nonlinear Robust Filtering of Sampled-Data Dynamical Systems

## TL;DR

This paper develops an LMI-based method for designing robust H-infinity observers for nonlinear sampled-data systems, ensuring convergence and robustness even with approximate models and uncertainties.

## Contribution

It introduces a novel LMI approach for robust observer design applicable to both exact and approximate discrete-time models of nonlinear systems.

## Key findings

- Observer convergence with exact models demonstrated
- Practical convergence achieved with Euler approximation
- Robustness against nonlinear uncertainties guaranteed

## Abstract

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 H_infty 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.