LMI-Based H∞ Observer Design for Nonlinear Lipschitz System

Abstract

The problem of circle criterion-based H∞ observer design for nonlinear systems is addressed in this article. An LMI-based observer is developed for the nonlinear Lipschitz systems with linear outputs under the presence of noise/disturbances. The proposed LMI condition is obtained by using reformulated Lipschitz property, standard Young's relation and a newly defined positive definite matrix multiplier. The inclusion of the matrix multiplier adds additional numbers of decision variables in the LMI, which provides extra degrees of freedom from a feasibility point of view. Further, the performance of the proposed observer is validated using numerical examples.