Estimation of basins of attraction for uncertain systems with affine and Lipschitz dynamics. (English) Zbl 1047.93043

Cruck, Eva; Moitie, Rodéric; Seube, Nicolas

Dyn. Control 11, No. 3, 211-227 (2001).

Summary: This paper is devoted to estimation and numerical approximation of basins of attraction for a class of uncertain systems. We consider systems described by a differential equation depending of a disturbance known by its bounds. By using viability theory tools, we derive lower and upper estimates of basins of attraction. We present numerical simulation results of the viability kernel algorithm to basin of attraction approximation problems.

MSC:

93D20	Asymptotic stability in control theory
34A60	Ordinary differential inclusions
49J53	Set-valued and variational analysis

Keywords:

basin of attraction; differential inclusions; uncertain systems; viability kernel algorithm