Dissipative control systems and disturbance attenuation for nonlinear H∞ problems

Applied Mathematics and Optimization

Volumn 40, Issue 2, 1999, Pages 163-181

  Frankowska, H ^a   Quincampoix, M ^b  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b UNIVERSITÉ DE BRETAGNE OCCIDENTALE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEM ANALYSIS; OPTIMAL CONTROL SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

DISSIPATIVE CONTROL SYSTEMS; ISAACS' EQUATION;

NONLINEAR CONTROL SYSTEMS;

EID: 0033181501     PISSN: 00954616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002459900120     Document Type: Article

References (16)

1. Aubin J-P (1991) Viability Theory. Birkhäuser, Boston
2. Aubin J-P, Cellina A (1984) Differential Inclusions. Springer-Verlag, New York
3. Aubin J-P, Frankowsa H (1990) Set-Valued Analysis. Birkhäuser, Boston
4. Barles G. (1993) Discontinuous viscosity solutions of first-order Hamilton-Jacobi equations: a guided visit. Nonlinear Anal Theory Appl 9:1123-1134
5. Barron EN, Evans, LC, Jensen R (1984) Viscosity solutions of Isaacs' equations and differential games with Lipschitz controls. J Differential Equations 53:213-233
6. Barron EN, Jensen R (1990) Semicontinuous viscosity solutions for Hamilton-Jacobi equations with convex Hamiltonians. Comm Partial Differential Equations 15(12):1713-1742
7. ∞-Optimal Control and Minimax Design Problems. Birkhäuser, Boston
8. Crandall MG, Evans LC, Lions, PL (1984) Some properties of viscosity solutions of Hamilton-Jacobi equations. Trans Amer Math Soc 282:487-502
9. Filippov AF (1958) On some problems of optimal control theory. Vestnik Moskov Univ, Math 2:25-32
10. (English translation (1962) SIAM J Control 1:76-84
11. Frankowska H (1993) Lower semicontinuous solutions to Hamilton-Jacobi-Bellman equations. SIAM J Control Optim 31(1):257-272
12. Frankowska H, Plaskacz S (1996) A measurable upper semicontinuous viability theorem for tubes. Nonlinear Anal TMA 26(3):565-582
13. Frankowska H, Plaskacz S, Rzezuchowski T (1995) Measurable viability theorems and Hamilton-Jacobi-Bellman equations. J Differential Equations 116(2):265-305
14. James MR (1993) A partial differential inequality for dissipative nonlinear systems. Systems Control Lett 21:315-320
15. Knobloch H, Flockerzi D (1995) Topics in Control Theory. Birkhäuser, Basel
16. Willems JC (1972) Dissipative dynamical systems. Arch Rational Mech Anal 45:321-351