This paper develops a new high-gain observer design method for nonlinear systems that has a lower gain compared to the standard high-gain observer. This new observer, called HG/LMI observer is obtained by combining the standard high gain methodology with the LMI-based observer design technique. Through analytical developments, the paper shows how the new observer provides lower gains, shows how it applies to systems with multi nonlinear functions and analyzes performance in the presence of measurement noise and/or delayed output measurements. A numerical example is given to illustrate the increasing advantage of the new HG/LMI observer with increase in the observer's "compromise index". Finally, the applicability and performance of the observer is demonstrated for a real-world application consisting of a train's magnetic levitation system.