Contents I. Introduction
A positive system is one whose state vectors remain nonnegative along its trajectories for any nonnegative initial conditions [1]. Since many physical systems have state variables that cannot assume negative values, positive systems arise in many practical applications such as economics, biology, chemistry, etc. For example, concentrations of reagents in a chemical reaction are clearly governed by positive dynamics. The stability of positive systems was investigated in [2]–[6]. Fornasini and Valcher [2] used a common linear copositive Lyapunov function
A Lyapunov function is an energy-like function that has a minimum at a stable equilibrium and a maximum at an unstable equilibrium. This property is used to obtain sufficient conditions for the stability or instability of a dynamic system.
to derive stability conditions for positive switched systems. Shim and Jo [3] discussed the stability of a family of equilibrium points, which are particularly of interest when positive systems undergo bifurcations. Stability analysis for positive systems with time-varying delays was addressed in [4] and [5]. Liu [6] proposed a control design for delayed positive systems, which results in a positive and stable closed-loop system. For more on positive systems and their properties, see [7].