Mathematical Problems in Engineering
Volume 2004 (2004), Issue 3, Pages 225-262
Vector dissipativity theory for large-scale impulsive dynamical systems
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.