Properties of Eventually Positive Linear Input-Output Systems

In this paper, we consider the so-called eventually positive systems, that is systems with trajectories originating in a positive orthant becoming positive after some finite transient. We extend this notion to the input-output system case. Our extension is performed in such a manner, that some valuable properties of internally positive input-output systems are preserved. For example, the stable systems have sum-separable Lyapunov functions, induced norms can be computed using linear programming and the energy functions have nonnegative derivatives.