Advances in Difference Equations
Volume 2004 (2004), Issue 1, Pages 37-66
doi:10.1155/S1687183904310071
Vector dissipativity theory for discrete-time large-scale nonlinear dynamical systems
Wassim M. Haddad1
, Qing Hui1
, Vijaysekhar Chellaboina3
and Sergey Nersesov1
1School of Aerospace Engineering, Georgia Institute of Technology, Atlanta 30332-0150, GA, USA
3Mechanical and Aerospace Engineering, University of Missouri-Columbia, Columbia 65211, MO, USA
Abstract
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.