LMI based model order reduction considering the minimum phase characteristic of the system

One usual method to solve the model order reduction problem is to minimize the H_∞-norm of the difference between the transfer function of the original system and the reduced one. In many papers, the minimization problem is solved using the Linear Matrix Inequality (LMI) approach. This paper deals with defining an extra matrix inequality constraint to guaranty that the minimum phase characteristic of the system preserves after order reduction. To overcome this, poles and zeros of the reduced system transfer function must be at Left-Half Plane (LHP). It is very easy to apply a LMI condition to force the poles of the system to be at LHP. However, the same cannot be applied to zeroes easily. Thus, a special state-space realization of the system is introduced in a way to apply conditions on zeros of the reduced system. The method is applied to some sample example and the simulation results verify the performance of the proposed method.