order reduction of linear systems with keeping the minimum phase charactristic of the system: lmi based approach

model order reduction is known as the problem of minimizing the -norm of the difference between the transfer function of the original system and the reduced one. in many papers, linear matrix inequality (lmi) approach is utilized to address the minimization problem. this paper deals with defining an extra matrix inequality constraint to guarantee 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 examples and the simulation results verify the performance of the proposed method.