# Dissipative Control Systems and Disturbance Attenuation for Nonlinear H{sup {infinity}} Problems

## 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{sup {infinity}} problem from contingent formulation of Isaacs' equation.

- Authors:

- CNRS and Centre de Recherches VJC, Universite Paris-Dauphine, Place du Marechal de Lattre de Tassigny, 75775 Paris cedex 16 (France)
- Departement de Mathematiques, Universite de Bretagne Occidentale, Avenue Le Gorgeu, B.P. 809, 29285 Brest cedex (France)

- Publication Date:

- OSTI Identifier:
- 21067544

- Resource Type:
- Journal Article

- Journal Name:
- Applied Mathematics and Optimization

- Additional Journal Information:
- Journal Volume: 40; Journal Issue: 2; Other Information: DOI: 10.1007/s002459900120; Copyright (c) 1999 Springer-Verlag New York Inc.; Article Copyright (c) Inc. 1999 Springer-Verlag New York; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0095-4616

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATTENUATION; CONTROL SYSTEMS; CONTROL THEORY; DISTURBANCES; FEEDBACK; FUNCTIONS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; PARTIAL DIFFERENTIAL EQUATIONS

### Citation Formats

```
Frankowska, H., and Quincampoix, M.
```*Dissipative Control Systems and Disturbance Attenuation for Nonlinear H{sup {infinity}} Problems*. United States: N. p., 1999.
Web. doi:10.1007/S002459900120.

```
Frankowska, H., & Quincampoix, M.
```*Dissipative Control Systems and Disturbance Attenuation for Nonlinear H{sup {infinity}} Problems*. United States. doi:10.1007/S002459900120.

```
Frankowska, H., and Quincampoix, M. Wed .
"Dissipative Control Systems and Disturbance Attenuation for Nonlinear H{sup {infinity}} Problems". United States. doi:10.1007/S002459900120.
```

```
@article{osti_21067544,
```

title = {Dissipative Control Systems and Disturbance Attenuation for Nonlinear H{sup {infinity}} Problems},

author = {Frankowska, H. and Quincampoix, M.},

abstractNote = {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{sup {infinity}} problem from contingent formulation of Isaacs' equation.},

doi = {10.1007/S002459900120},

journal = {Applied Mathematics and Optimization},

issn = {0095-4616},

number = 2,

volume = 40,

place = {United States},

year = {1999},

month = {9}

}

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