Robust Control Design for Nonlinear Plants Based on Homogeneous Right Coprime Factorization and Sliding Mode Control

This paper investigates the problem of robust controller design for a homogeneous nonlinear plant with non-Lipschitz continuity, where unmodeled dynamics and external disturbances are presented. For the robust control for such a plant, a comprehensive design method based on homogeneous right coprime factorization (RCF) and sliding mode control is proposed. Firstly, a nonlinear plant is factorized as two stable operators by RCF. By analyzing the homogeneity degree of the system, a framework for RCF that precisely matches it is established, namely, a homogeneous RCF is established. On this basis, the stability of the system is ensured by a pair of designed stable operators satisfying the Bezout Identity. The designed two operators matches the homogeneity of the factorized operators. Furthermore, a composite controller structure is designed, which includes a nominal term based on a reference model using sliding mode control, and a robust compensation term based on the Bezout Identity. Simulation results demonstrate that the designed controller effectively exhibits robustness and stability in the presence of uncertainties, disturbances and achieves tracking performance of reference signals.