Open Access

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

  • Wassim M Haddad1Email author,
  • Qing Hui1,
  • Vijaysekhar Chellaboina2 and
  • Sergey Nersesov1
Advances in Difference Equations20042004:612830

DOI: 10.1155/S1687183904310071

Received: 15 October 2003

Published: 24 March 2004


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.

Authors’ Affiliations

School of Aerospace Engineering, Georgia Institute of Technology
Mechanical and Aerospace Engineering, University of Missouri-Columbia


© Haddad et al. 2004