Advertisement

Stability of Large Scale Interconnected Systems

  • Jan C. Willems

Abstract

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).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. |1|.
    Willems, J.C., “Qualitative Behavior of Interconnected Systems”, Annals of Systems Research, Vol. 3, pp. 61–80, 1973Google Scholar
  2. |2|.
    Willems, J.C, J.C., “Mechanisms for the Stability and Instability in Feedback Systems”, Proceedings IEEE, Vol. 64, No.1, 1976Google Scholar
  3. |3|.
    Kaiman, R.E., Falb, P.L., and Arbib, M.A., Topics in Mathematical System Theory, McGraw-Hill, 1969Google Scholar
  4. |4|.
    Desoer, C.A., Notes for a Second Course on Linear Systems, Van Nostrand-Reinhold, 1970Google Scholar
  5. |5|.
    Willems, J.L., Stability Theory of Dynamical Systems, Nelson, 1970Google Scholar
  6. |6|.
    Willems, J.C., “Dissipative Dynamical Systems, Part 1: General Theory; Part II: Linear Systems with Quadratic Supply Rates”, Arch. Rat. Mech. and Analysis, Vol. 45, pp. 321–351 and 352–392, 1972Google Scholar
  7. |7|.
    Willems, J.C., “The Construction of Lyapunov Functions for Input/Output Stable Systems” SIAM J. Control, Vol. 9, pp. 105–134, 1971CrossRefGoogle Scholar
  8. 8.
    Siljak, D.D., “Connective Stability of Competitive Equilibrium”, Automatical Vol. 11, 1975Google Scholar
  9. 9.
    Cook, P.A., “The Stability of Interconnected Systems”, Int. J. Control, Vol. 20, pp. 407–415, 1974CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1976

Authors and Affiliations

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

Personalised recommendations