Properties of Eventually Positive Linear Input-Output Systems
For control theorists, this provides a new class of systems with tractable analysis tools, though the extension is incremental.
The paper extends the concept of eventually positive systems to input-output systems, preserving properties like computable induced norms via linear programming and nonnegative derivatives of energy functions.
In this paper, we consider the systems with trajectories originating in the nonnegative orthant becoming nonnegative after some finite time transient. First we consider dynamical systems (i.e., fully observable systems with no inputs), which we call eventually positive. We compute forward-invariant cones and Lyapunov functions for these systems. We then extend the notion of eventually positive systems to the input-output system case. Our extension is performed in such a manner, that some valuable properties of classical internally positive input-output systems are preserved. For example, their induced norms can be computed using linear programming and the energy functions have nonnegative derivatives.