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Applied Mathematics and Optimization

, Volume 40, Issue 2, pp 163–181 | Cite as

Dissipative Control Systems and Disturbance Attenuation for Nonlinear H Problems

  • H. Frankowska
  • M. Quincampoix

Abstract.

We characterize functions satisfying a dissipative inequality associated with a control problem. Such a characterization is provided in terms of an epicontingent solution, or a viscosity supersolution to a partial differential equation called Isaacs' equation. Links between supersolutions and epicontingent solutions to Isaacs' equation are studied. Finally, we derive (possibly discontinuous) disturbance attenuation feedback of the H problem from contingent formulation of Isaacs' equation.

Key words. Isaacs' equation, H∞ problem, Contingent and viscosity solutions to PDEs. AMS Classification. 93B36, 93B52, 93C10, 93C15, 34A60, 35R45. 

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Copyright information

© Springer-Verlag New York Inc. 1999

Authors and Affiliations

  • H. Frankowska
    • 1
  • M. Quincampoix
    • 2
  1. 1.CNRS and Centre de Recherches VJC, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France FR
  2. 2.Département de Mathématiques, Université de Bretagne Occidentale, Avenue Le Gorgeu, B.P. 809, 29285 Brest cedex, FranceFR

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