The Observer Design for Lipschitz Nonlinear Systems Based on LMI

This paper deals with the design methods of full-order and reduced-order observers for Lipschitz nonlinear systems. Under the assumption that a LMI is feasible, we point out there exists a full-order observer. By a way of coordinate transformation, we also put forward a design approach of reduced-order observer under the some assumption and the gain matrix of reduced-order observer is based on the solution of the LMI. The developed theory is used successfully in the design of an observer for a flexible joint robotic system