Mathematical Problems in Engineering
Volume 8 (2002), Issue 6, Pages 493-515

Hybrid nonnegative and computational dynamical systems

Wassim M. Haddad,1 Vijaysekhar Chellaboina,2 and Sergey G. Nersesov1

1School of Aerospace Engineering, Georgia Institute of Technology, Atlanta 30332-0150, GA, USA
2Mechanical and Aerospace Engineering, University of Missouri, Columbia 65211, MO, USA

Received 26 March 2002

Copyright © 2002 Wassim M. Haddad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 functions 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.