Stability of Large Scale Interconnected Systems

  • Jan C. Willems


A large scale system may be defined as an interconnection of a large number of individual subsystems. Usually the dynamic features of the system stem practically always from the component subsystems and the interconnection laws simply identify the signal flow graph between the various subsystems. The complexity of the system is in the first place due to these interconnections and makes it usually very hard to predict the overall behavior of the interconnected system. A desirable feature of an analysis or synthesis procedure for large scale systems is the separation of these two levels. One thus likes an analysis or synthesis procedure to be based, on the one hand, on the “local” subsystems (through the construction of, say, Lyapunov functions for the local subsystems or the design of dynamic controllers around these local subsystems) and, on the other hand, on the “global” interconnection laws (through the analysis of these interconnection laws, or, in the case of synthesis, through the design of the signal flow graph which specifies how the physical interaction is and how information it to be transmitted between the subsystems).


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Copyright information

© Plenum Press, New York 1976

Authors and Affiliations

  • Jan C. Willems
    • 1
  1. 1.Mathematical InstituteUniversity of GroningenGroningenThe Netherlands

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