Initial research on stability margin of nonlinear systems under additive-state-decomposition-based control framework

The study on the stability margin of nonlinear systems is difficult and meaningful. This paper makes an initial research on the stability margin for a nonlinear system with the unmodeled higher-order uncertainty. Three stabilizing control methods are tried, and the additive-state-decomposition-based control is the best compared with the other two. The first control method is the feedback linearization control, which may lead to a singularity problem. To avoid the singularity, a backstepping controller is further designed. However, it is still hard to analyze the system stability margin due to the nonlinearity. For such a purpose, the third control method, namely additive-state-decomposition-based control, is proposed to overcome both problems above. Under the additive-state-decomposition-based control framework, the stability margin of the nonlinear system is studied by the Bode plot method, which can be realized via a data-driven method. Finally, a series compensator is designed to compensate for the unmodeled higher-order uncertainty, and make the system stability margin satisfy the design specification. The comparison of the three methods and the verification of the validity of stability margin are illustrated by the simulation.