Positive Realizations of Transfer Matrices With Real Poles

In this brief, we prove that any normal transfer matrix with nonnegative impulse response and simple real poles of second order in discrete-time linear systems admits a minimal positive realization. This result can be used to obtain a minimal positive realization of some transfer matrices of any order with simple real poles. In addition, several results obtained for single-input single-output systems are adapted to solve the positive realization problem of transfer matrices with multiple real poles in multiple-input multiple-output systems.