Electrical & Computer Engineering, Department of


Date of this Version



2004 Hindawi Publishing Corporation


Mathematical Problems in Engineering 2004:3 (2004) 225–262 2000 Mathematics Subject Classification: 93D30, 93A15, 93C10, 34A37 URL: http://dx.doi.org/10.1155/S1024123X04310021


Modern complex large-scale impulsive systems involvemultiplemodes 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 subsystemdynamics 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.