Mathematical Problems in Engineering
Volume 2004 (2004), Issue 3, Pages 225-262

Vector dissipativity theory for large-scale impulsive dynamical systems

Wassim M. Haddad,1 VijaySekhar Chellaboina,2 Qing Hui,1 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 17 October 2003; Revised 30 March 2004

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.


Modern complex large-scale impulsive systems involve multiple modes of operation placing stringent demands on controller analysis of increasing complexity. In analyzing these large-scale systems, it is often desirable to treat the overall impulsive system as a collection of interconnected impulsive subsystems. Solution properties of the large-scale impulsive system are then deduced from the solution properties of the individual impulsive subsystems and the nature of the impulsive system interconnections. In this paper, we develop vector dissipativity theory for large-scale impulsive dynamical systems. Specifically, using vector storage functions and vector hybrid supply rates, dissipativity properties of the composite large-scale impulsive systems are shown to be determined from the dissipativity properties of the impulsive subsystems and their interconnections. Furthermore, extended Kalman-Yakubovich-Popov conditions, in terms of the impulsive 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 large-scale impulsive dynamical systems using vector Lyapunov functions.