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Dissipative Control Systems and Disturbance Attenuation for Nonlinear H ∞ Problems

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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.

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Authors and Affiliations

  1. CNRS and Centre de Recherches VJC, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France , , , , , , FR

    H. Frankowska

  2. Département de Mathématiques, Université de Bretagne Occidentale, Avenue Le Gorgeu, B.P. 809, 29285 Brest cedex, France, , , , , , FR

    M. Quincampoix

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  1. H. Frankowska
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  2. M. Quincampoix
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Accepted 20 January 1998

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Frankowska, H., Quincampoix, M. Dissipative Control Systems and Disturbance Attenuation for Nonlinear H ∞ Problems. Appl Math Optim 40, 163–181 (1999). https://doi.org/10.1007/s002459900120

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  • DOI: https://doi.org/10.1007/s002459900120

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