Dissipative Distributed Systems

  • Jan C. Willems
  • Harish K. Pillai
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 134)


The notion of a dissipative system is among one of the more useful concepts in systems theory. It may be viewed as a natural generalization of a Lyapunov function to ‘open’ systems. Many results involving stability of systems and design of robust controllers make use of this notion. The theory of dissipative systems has been developed mainly for systems that have time as its only independent variable (1-D systems). However, models of physical systems often have several independent variables (i.e., they are n-D systems), for example, time and space variables. In this paper we develop the theory of dissipative systems for n-D systems.


Dissipation Rate Image Representation Dissipative System Polynomial Matrix Manifest Variable 
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Copyright information

© Springer-Verlag New York, Inc. 2003

Authors and Affiliations

  • Jan C. Willems
    • 1
  • Harish K. Pillai
    • 2
  1. 1.Department of Electrical EngineeringUniversity of LeuvenLeuven-HeverleeBegium
  2. 2.Department of Electrical EngineeringIndian Institute of TechnologyBombay, Powai, MumbaiIndia

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