Robust H infinity model reference tracking control of singular systems using T-S fuzzy model and LMI

Abstract

In this study, a Takagi-Sugeno fuzzy model based tracking controller is proposed for nonlinear high index singular systems with a guaranteed H1 model reference tracking performance. A coordinate transformation is introduced, which allows to represent the nonlinear high index singular systems using T-S fuzzy model. This transformation facilitates the specification of a dynamic reference system that satisfies the same constraints as the actual system. Moreover, the proposed transformation relaxes the existence condition of a full order observer for a nonlinear high index singular system. A modification of the existing linear matrix inequality optimization algorithm has been proposed to make the algorithm compatible for singular systems. The proposed approach is general and can be used for designing the tracking controller and defining the dynamic reference model for any singular systems with any index. Without using the exact feedback linearization technique and complicated adaptive schemes, this tracking controller design approach is simple and feasible for practical applications. Finally, two high index singular systems from two different fields are used as examples to demonstrate the proposed design effectiveness.