Multi-input nonlinear affine systems represented in a canonical (normal)
form are considered. The controls are assumed to be constrained.
The application of feedback linearization results in a closed-loop system
that is decomposed into an aggregate of independent linear subsystems
in a neighborhood of the origin and is nonlinear when controls reach
saturation. For the closed-loop system obtained, the problem of estimating
the attraction domain is set. A method for constructing an
estimate of the attraction domain that is based on results of absolute
stability theory is suggested. An estimate is sought as a Cartesian
product of invariant ellipsoids each of which is found by solving a system
of linear matrix inequalities. An optimization problem of finding
the best estimate is posed. The discussion is illustrated by numerical
examples.