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 anapriori positivity constraint on the processing algorithm isatoo 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 andastraightforward 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.