Nonlinear Control Method for Nonlinear Systems with Unknown Perturbations by Combining Left and Right Factorization

Abstract

AbstractIn this paper, nonlinear control design scheme for a class of nonlinear systems is proposed based on operator coprime factorization theory. In detail, two stable controllers are provided to design a Bezout identity by combining left factorization (not coprime) with right factorization. Based on the proposed design method, a realization approach to left coprime factorization for the nonlinear system is obtained, which provides an effective framework for constructing left coprime factorization. Meanwhile, internal‐output stability of the nonlinear system is guaranteed. After that, based on the obtained left coprime factorization, the cases of the nonlinear systems with perturbations are discussed for guaranteeing robust stability for the perturbed systems. For the perturbations, two different cases, known bounded perturbations and unknown bounded perturbations, are investigated from different viewpoints to analyze robust stability issue for the perturbed systems. Finally, a simulation example is given to confirm the effectiveness of the proposed design method.