LMI Feasibility Analysis in Observer Design for Some Families of Nonlinear Systems

This note deals with observer design for nonlinear systems via Linear Matrix Inequalities (LMIs). The main goal consists of showing that for some families of nonlinear systems, the LMI-based observer design techniques always provide exponential convergent observer. Indeed, until now, this advantageous feature is unique to some types of observers/estimators, such as the high-gain observer, the sliding mode observer, and the moving horizon estimator, under certain conditions of detectability or observability. More specifically, the LMI conditions we propose in this paper always provide solutions to both systems in companion form and feedforward structure. An extension to a general class of nonlinear triangular systems without linear components is provided, which renders the applicability of LMI-based methods possible for a wide class of nonlinear systems without the need for nonlinear diffeomorphism-based transformations.