Optimal fixed-structure control for linear nonnegative dynamical systems

In this paper we develop optimal output feedback controllers for set-point regulation of linear nonnegative dynamical systems. Specifically, using a constrained fixed-structure control framework we develop optimal output feedback control laws that guarantee that the trajectories of the closed-loop system remain in the nonnegative orthant of the state space for nonnegative initial conditions. In addition we characterize domains of attraction predicated on closed and open Lyapunov level surfaces contained in the nonnegative orthant for unconstrained optimal linear-quadratic output feedback controllers. Output feedback controllers for compartmental systems with nonnegative inputs are also given.