Stabilizing a class of nonlinear systems based on approximate feedback linearization

Abstract

We present a method of stabilizing a class of nonlinear systems which are not necessarily feedback linearizable. First, we show a new way of constructing a diffeomorphism to transform a class of nonlinear systems to the feedback linearized form with perturbation. Then, we propose a semi-globally stabilizing control law for nonlinear systems that are connected by a chain of integrator perturbed by arbitrary nonlinear terms. In our approach, we have flexibility in choosing a diffeomorphism where the system is not restricted to involutivity and this leads to reduction in computational burden and flexibility in controller design.