Weakly positive continuous-time linear systems (Q1269842)

Singular continuous-time linear systems (descriptor systems) are considered in this paper. Such systems are called ``weakly positive'' if additional conditions are satisfied: the system matrix must be a Metzler matrix, the elements of the other matrices are nonnegative. The reduction of weakly positive systems into positive standard systems is investigated. Conditions for the existence of a suitable equivalence transformation are derived. The theory presented in the paper is applied to linear electrical circuits. It is shown that linear electrical circuits consisting of resistances, inductances and source voltages can be reduced to positive standard systems.