Viability Kernel of Control Systems

  • Jean-Pierre Aubin
  • Hélène Frankowska
Part of the Progress in Systems and Control Theory book series (PSCT, volume 9)


Existence of viable (controlled invariant) solutions of a control system is investigated by using the concept of viability kernel of a set (largest closed controlled invariant subset.) Results are exploited to prove convergence of a modified version of the zero dynamics algorithm to a closed viability domain. This is needed to obtain dynamical feedbacks, i.e., differential equations governing the evolution of viable controls. Among such differential equations, the one leading to heavy solutions (in the sense of heavy trends), governing evolution of controls with minimal velocity is singled out.


Differential Inclusion Singular System Viable Solution Zero Dynamic Contingent Cone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Jean-Pierre Aubin
    • 1
  • Hélène Frankowska
    • 1
  1. 1.CEREMADEUniversité Paris-DauphineParisFrance

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