Operator-based robust stability for nonlinear systems with multiple uncertainties using coprime factorisation method

In this paper, the robust stability of nonlinear systems with multiple uncertainties is considered by using a composite operator-based coprime factorisation method. Firstly, as for the exogenous external disturbance, the disturbance model is considered and the disturbance output is guaranteed to be bounded. Meantime, the adverse effect resulting from it is transformed to an equivalent effect on the stable part of the systems. By using operator-based coprime factorisation method, a feasible framework on multiple uncertainties is obtained. Then, the obtained equivalent effects resulting from the modelled disturbance and adverse effect from the internal perturbation are unified and addressed. Thirdly, sufficient conditions on guaranteeing robust stability of the considered nonlinear systems are considered by using robust coprime factorisation method, for relaxing computation burden on Bezout identity and avoiding requirement on knowing the perturbation signal. Based on the proposed conditions, two controllers are designed and the robust stability of the considered systems is proved. Finally, simulation results are shown to explain the proposed design scheme and confirm its effectiveness of this paper.