Advances in Difference Equations
Volume 2004 (2004), Issue 1, Pages 37-66

Vector dissipativity theory for discrete-time large-scale nonlinear dynamical systems

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

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

Received 15 October 2003

Copyright © 2004 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.


In analyzing large-scale systems, it is often desirable to treat the overall system as a collection of interconnected subsystems. Solution properties of the large-scale system are then deduced from the solution properties of the individual subsystems and the nature of the system interconnections. In this paper, we develop an analysis framework for discrete-time large-scale dynamical systems based on vector dissipativity notions. Specifically, using vector storage functions and vector supply rates, dissipativity properties of the discrete-time composite large-scale system are shown to be determined from the dissipativity properties of the subsystems and their interconnections. In particular, extended Kalman-Yakubovich-Popov conditions, in terms of the subsystem dynamics and interconnection constraints, characterizing vector dissipativeness via vector system storage functions are derived. Finally, these results are used to develop feedback interconnection stability results for discrete-time large-scale nonlinear dynamical systems using vector Lyapunov functions.