M. Bardi and I. C. Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi- Bellman equations. Systems and Control: Foundations and Applications, 1997.

M. Bardi and P. Soravia, Hamilton-Jacobi equations with singular boundary conditions on a free boundary and applications to differential games, Transactions of the American Mathematical Society, vol.325, issue.1, pp.205-229, 1991.
DOI : 10.1090/S0002-9947-1991-0991958-X

E. N. Barron and R. Jensen, Semicontinuous Viscosity Solutions For Hamilton???Jacobi Equations With Convex Hamiltonians, Communications in Partial Differential Equations, vol.10, issue.12, pp.1713-1742, 1990.
DOI : 10.1007/BF02765025

T. Basar and P. Bernard, Optimal Control and Related Minimax Design Problems, 1995.

L. D. Berkovitz, Differential Games of Generalized Pursuit and Evasion, SIAM Journal on Control and Optimization, vol.24, issue.3, pp.361-373, 1986.
DOI : 10.1137/0324021

J. V. Breakwell, Lecture notes, Differential Games and Applications, pp.70-95, 1977.
DOI : 10.1007/BFb0009064

F. Camilli, A. Cesaroni, L. Grüne, and F. Wirth, STABILIZATION OF CONTROLLED DIFFUSIONS AND ZUBOV'S METHOD, Stochastics and Dynamics, vol.06, issue.03, pp.373-393, 2006.
DOI : 10.1142/S0219493706001803

F. Camilli and L. Grüne, Characterizing attraction probabilities via the stochastic Zubov equation, Discrete Contin. Dyn. Syst. Ser. B, vol.3, issue.3, pp.457-468, 2003.

F. Camilli, L. Grüne, and F. Wirth, A Generalization of Zubov's Method to Perturbed Systems, SIAM Journal on Control and Optimization, vol.40, issue.2, pp.496-515, 2001.
DOI : 10.1137/S036301299936316X

F. Camilli, L. Grüne, and F. Wirth, A regularization of Zubov???s equation for robust domains of attraction, Nonlinear control in the year 2000, pp.277-289, 2001.
DOI : 10.1007/BFb0110220

F. Camilli, L. Grüne, and F. Wirth, Construction of Lyapunov functions on the domain of asymptotic nullcontrollability: numerics, Proceedings of NOLCOS 2004, pp.883-888, 2004.

F. Camilli, L. Grüne, and F. Wirth, Control Lyapunov Functions and Zubov's Method, SIAM Journal on Control and Optimization, vol.47, issue.1, pp.301-326, 2008.
DOI : 10.1137/06065129X

P. Cardaliaguet, A Differential Game with Two Players and One Target, SIAM Journal on Control and Optimization, vol.34, issue.4, pp.1441-1460, 1996.
DOI : 10.1137/S036301299427223X

P. Cardaliaguet, Nonzero-sum differential games revisited. working paper, 2005.

R. J. Elliott and N. J. Kalton, The existence of value in differential games, Memoirs of the American Mathematical Society, vol.0, issue.126, 1972.
DOI : 10.1090/memo/0126

R. J. Elliott and N. J. Kalton, Cauchy problems for certain Isaacs-Bellman equations and games of survival, Transactions of the American Mathematical Society, vol.198, pp.45-72, 1974.
DOI : 10.1090/S0002-9947-1974-0347383-8

W. H. Fleming and H. M. Soner, Controlled Markov processes and viscosity solutions, Applications of Mathematics, vol.25, 2006.

A. Friedman, On the definition of differential games and the existence of value and of saddle points, Journal of Differential Equations, vol.7, issue.1, pp.69-91, 1970.
DOI : 10.1016/0022-0396(70)90124-5

L. Grüne, Asymptotic behavior of dynamical and control systems under perturbation and discretization , volume 1783 of Lecture Notes in Mathematics, 2002.

L. Grüne, W. Semmler, and L. Bernard, Firm value, diversified capital assets, and credit risk: towards a theory of default correlation, J. Credit Risk, vol.3, pp.81-10908, 2007.

L. Grüne and F. Wirth, Computing control Lyapunov functions via a Zubov type algorithm, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), pp.2129-2134, 2000.
DOI : 10.1109/CDC.2000.914109

R. Isaacs, Differential games. A mathematical theory with applications to warfare and pursuit, control and optimization, The SIAM Series in Applied Mathematics) John Wiley and Sons, 1965.

H. K. Khalil, Nonlinear systems, 1996.

N. N. Krasovskij and A. I. Subbotin, Game-theoretical control problems. Transl. from the Russian by Samuel Kotz, 1988.

V. Lakshmikantham and S. Leela, Differential and integral inequalities: Theory and applications . Vol. I: Ordinary differential equations, Mathematics in Science and Engineering, p.55, 1969.

M. Malisoff, Further results on Lyapunov functions and domains of attraction for perturbed asymptotically stable systems, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal, vol.12, issue.2, pp.193-225, 2005.

N. N. Petrov, On the existence of a pursuit game value, Sov. Math., Dokl, vol.11, pp.292-294, 1970.

S. Plaskacz and M. Quincampoix, Value-functions for Differential Games and Control Systems with Discontinuous Terminal Cost, SIAM Journal on Control and Optimization, vol.39, issue.5, pp.1485-1498, 2001.
DOI : 10.1137/S0363012998340387

O. S. Serea, Discontinuous differential games and control systems with supremum cost, Journal of Mathematical Analysis and Applications, vol.270, issue.2, pp.519-542, 2002.
DOI : 10.1016/S0022-247X(02)00087-2

URL : http://doi.org/10.1016/s0022-247x(02)00087-2

E. D. Sontag, A Lyapunov-Like Characterization of Asymptotic Controllability, SIAM Journal on Control and Optimization, vol.21, issue.3, pp.462-471, 1983.
DOI : 10.1137/0321028

E. D. Sontag, Comments on integral variants of ISS, Systems & Control Letters, vol.34, issue.1-2, pp.93-100, 1998.
DOI : 10.1016/S0167-6911(98)00003-6

E. D. Sontag, Stability and stabilization: discontinuities and the effect of disturbances In Nonlinear analysis, differential equations and control, NATO Sci. Ser. C Math. Phys. Sci, vol.528, pp.551-598, 1998.

E. D. Sontag and Y. Wang, New characterizations of input-to-state stability, IEEE Transactions on Automatic Control, vol.41, issue.9, pp.1283-1294, 1996.
DOI : 10.1109/9.536498

P. Soravia, Pursuit???Evasion Problems and Viscosity Solutions of Isaacs Equations, SIAM Journal on Control and Optimization, vol.31, issue.3, pp.604-623, 1993.
DOI : 10.1137/0331027

P. Soravia, Stability of Dynamical Systems with Competitive Controls: The Degenerate Case, Journal of Mathematical Analysis and Applications, vol.191, issue.3, pp.428-449, 1995.
DOI : 10.1006/jmaa.1995.1139

F. Wirth, A Linearization Principle for Robustness with Respect to Time-Varying Perturbations, Dynamics, Bifurcations, and Control, pp.191-200, 2002.
DOI : 10.1007/3-540-45606-6_13

V. I. Zubov, Methods of A. M. Lyapunov and their application. Translation prepared under the auspices of the United States Atomic Energy Commission, 1964.