A generalization of Zubov's method to perturbed systems

L. Grüne, F. Camilli, F. Wirth: A generalization of Zubov's method to perturbed systems
SIAM Journal on Control and Optimization 40, 496 - 515, 2001

DOI: 10.1137/S036301299936316X
Keywords: asymptotic stability; Zubov's method; robust stability; domain of attraction; viscosity solutions
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Abstract:

A generalization of Zubov's theorem on representing the domain of attraction via the solution of a suitable partial differential equation is presented for the case of perturbed systems with a singular fixed point. For the construction it is necessary to consider solutions in the viscosity sense. As a consequence maximal robust Lyapunov functions can be characterized as viscosity solutions.

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