Robust Fuzzy Output Regulator Design for Nonlinear Systems without Virtual Desired Variable Calculation

Abstract

This paper proposes a robust T-S fuzzy output regulator for affine nonlinear systems in the presence of parametric uncertainties and external disturbance. First, we introduce the fuzzy output regulator by involving an integral error state and PDC compensation, where a set of virtual desired variables (VDVs) is solved for error coordinate transformation. The benefit of the VDV-based regulator is with systematic design. However, since the VDV-based fuzzy regulator is unavailable when the system is subject to uncertainty and external disturbance, the controller is further reduced to the non-VDV fuzzy output regulator. The VDV calculation is removed in a more simplified manner, while the asymptotical exponential output regulation is assured. To reject uncertainty and external disturbance, the robust $H_\infty$ theorem is derived with linear matrix inequality (LMI) stability condition. Finally, numerical simulation of the DC-DC buck converter is given to show the benefits of the non-VDV fuzzy output regulator.