Observer Design for Nonlinear Systems: A Tutorial

Abstract

This tutorial will describe the design of stable observers for nonlinear systems. The design methodology utilizes tools that include Lyapunov analysis, the Circle Criterion and the S-procedure Lemma. The observer stability conditions are typically obtained as linear or bilinear matrix inequalities from which the observer gains can be computed. The tutorial will start with a dynamic system in which the process dynamics has Lipschitz nonlinearities. This will later be generalized to allow for either Lipschitz, bounded Jacobian or sector bounded nonlinearities in both the process dynamics and the measurement equations. Simple programs to solve LMIs in Matlab and obtain the observer gains will also be presented. The lecture will conclude with the application of the developed methodology to automotive slip angle estimation in the presence of nonlinear tire force models.