Representation of a Class of MIMO Systems via Internally Positive Realization

In some technological frame-works, such as Charge Routing Networks (CRNs), or fiber-optic filters, only positive state space realizations of digital signal processing algorithms, such as filters or control laws, can be implemented. On the other hand, the imposition of an a priori positivity constraint on the processing algorithm is a too strong design limitation. For this reason, some authors studied the problem of state-space realization of generic stationary filters through combination of positive systems, in the discrete-time framework. The single-input/single-output (SISO) case has been widely investigated and important results are available in the literature. On the contrary, no specific theoretical results exist for multi-input/multi-output (MIMO) systems. In this paper, the problem of the Internal Positive Realization (IPR) of MIMO systems and filters is formulated and a straightforward method for the construction of IPRs is proposed. The stability properties of the resulting positive realization are also investigated. The method is illustrated on two engineering applications.