Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2004 / Article

Open Access

Volume 2004 |Article ID 579046 | https://doi.org/10.1155/S1024123X04310021

Wassim M. Haddad, VijaySekhar Chellaboina, Qing Hui, Sergey Nersesov, "Vector dissipativity theory for large-scale impulsive dynamical systems", Mathematical Problems in Engineering, vol. 2004, Article ID 579046, 38 pages, 2004. https://doi.org/10.1155/S1024123X04310021

Vector dissipativity theory for large-scale impulsive dynamical systems

Received17 Oct 2003
Revised30 Mar 2004

Abstract

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.

Copyright © 2004 Hindawi Publishing Corporation. 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.


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