State space representation of a class of MIMO systems via combination of positive systems

In many technological frameworks the only choice to implement the designed signal processing scheme (filter or control law) is to provide a positive state-space realization. On the other hand, by setting an a priori positivity constraint to the processing algorithm could be a heavy restriction to its performances. It is worthwhile, then, to look for a state-space realization through combination of positive systems. In this paper a state-space representation for a class of MIMO systems is proposed in the discrete-time framework. The approach followed provides an easy implementation by means of combinations of positive systems, whose total order is fixed regardless of the poles location in the complex plane. The stability of the positive realization of a stable system is also investigated.