Characterization and Stability of Autonomous Positive Descriptor Systems

This note addresses two problems: the characterization of positivity of autonomous descriptor systems and the problem of finding conditions for their stability. For these fundamental issues, we provide necessary and sufficient conditions complemented with a numerically reliable computational approach. The given conditions can be checked by means of linear programming (LP). Also, we derive a necessary and sufficient condition for stability that is connected to the underlying eigenstructure of the system.