A construction method for positive realizations with an order bound

This paper presents an efficient construction method to address the positive realization problem with an order bound for primitive transfer functions with multiple real or complex conjugate pairs of poles using polyhedral cone concepts. Through a down-sampling step, the non-primitive transfer function is decomposed into a sum of primitive transfer functions. A construction method for the positive realization of a primitive transfer function with multiple poles is proposed by using a regular polygon in the complex plane. A sufficient condition for the existence of the positive realization with an order bound is analyzed. Numerical examples are provided to demonstrate the efficiency of the proposed method for obtaining positive realizations.