On the use of quasi-positive versus positive state-space models of externally positive discrete-time systems

Positive state-space models describe large classes of processes in econometry, epidemiology, biology, ecology, chemistry, hydraulics and logistics. These models satisfy strict algebraic conditions that can be directly fulfilled when the models are obtained by means of traditional modeling techniques by selecting the state variables in a “natural” way i.e. by associating a well-defined physical meaning to every variable. The situation is more critical when positive state-space models must be obtained by means of realization techniques from transfer functions since, in this case, the fulfillment of positivity conditions could call for the introduction of spurious dynamics and non minimal parameterizations. A possible alternative consists in using quasi-positive models; this paper discusses the pros and cons of these solutions.