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

This letter deals with observer design for a class of nonlinear systems. This letter 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.