Hybrid nonnegative and compartmental dynamical systems

Nonnegative and compartmental dynamical systems are governed by conservation laws and are comprised of homogeneous compartments which exchange variable nonnegative quantities of material via intercompartmental flow laws. These systems typically possess hierarchical (and possibly hybrid) structures and are remarkably effective in capturing the phenomenological features of many biological and physiological dynamical systems. In this paper we develop several results on stability and dissipativity of hybrid nonnegative and compartmental dynamical systems. Specifically, using linear Lyapunov functions we develop sufficient conditions for Lyapunov and asymptotic stability for hybrid nonnegative dynamical systems. In addition, using linear and nonlinear storage ftmctions with linear hybrid supply rates we develop new notions of dissipativity theory for hybrid nonnegative dynamical systems. Finally, these results are used to develop general stability criteria for feedback interconnections of hybrid nonnegative dynamical systems.