Estimation of Attraction Domains for Multi-Input Affine Systems with Constrained Controls

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.