Minimal Strongly Eventually Positive Realization for a Class of Externally Positive Systems

摘要

The minimal positive realization of externally positive systems is still an open problem due to various restrictions caused by the nonnegativity constraint on the state-space matrices. In this paper. the minimal strongly eventually positive realization, which relaxes the nonnegativity constraint on the state-space model and only requires that the state trajectory is nonnegative after a certain number of steps, is proposed for an externally positive system. It is shown that a discrete-time transfer function with a simple strictly dominant root is externally positive if and only if it has a minimal strongly eventually positive realization. A constructive proof is provided. The continuous-time counterpart is also addressed by transforming it into a corresponding discrete-time case.