Stability and dissipativity theory for discrete-time nonnegative and compartmental dynamical systems

Nonnegative and compartmental dynamical systems are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative. These models are widespread in engineering, biomedicine, and ecology. In this paper we develop several results on stability and dissipativity of discrete-time linear and nonlinear nonnegative dynamical systems. Specifically, using linear Lyapunov functions we develop necessary and sufficient conditions for Lyapunov stability and asymptotic stability for nonnegative systems. In addition, using linear storage functions and linear supply rates we develop new notions of dissipativity theory for nonnegative dynamical systems.