A New LMI Based H∞ Observer Design Method for Lipschitz Nonlinear Systems

This note deals with H-infinity observer design for Lipschitz nonlinear systems. Thanks to a new and judicious use of the Young's relation, new and less conservative LMI conditions are proposed to solve the problem of observer design. Two LMI design methods are provided. First, we propose a new enhanced LMI technique that allows to improve the standard LMI methods for Lipschitz systems. A second method is proposed to improve more the first one. It consists in combining the first method and the well known LPV approach. This technique exploits the advantages of the LPV approach for larger Lipschitz constants and in the second time, it allows to reduce the high number of LMIs of the classical LPV method. An application to a neural mass model is presented to show the effectiveness of the proposed method.