LMI-Based Observer Design for Non-Globally Lipschitz Systems Using Kirszbraun–Valentine Extension Theorem

Abstract

This paper deals with observer design for a class of nonlinear systems. The paper makes two notable contributions. First, we propose a solution to design an observer for systems without global Lipschitz conditions by extending the nonlinearities to globally Lipschitz functions. Secondly, we provide a novel Linear Matrix Inequality (LMI) condition ensuring asymptotic convergence of the observer. The extension of the nonlinearities is achieved by exploiting old mathematical tools on Kirszbraun-Valentine Lipschitz extensions. Once the structure of the observer, based on the extended functions, is well-posed, we propose a new LMI technique, which is more general and more convenient than those existing in the literature.