Stable Controller Design for T–S Fuzzy Control Systems with Piecewise Multi-linear Interpolations into Membership Functions

Abstract

This paper focuses on stabilization of T–S fuzzy control systems. We use the information of the premises of the T–S fuzzy control systems to reduce the conservativeness of the stabilization conditions. First, the membership functions (MFs) in the premises are approximated with their piecewise multi-linear interpolations. In this way, different types of MFs can be tackled in a unified approach. We use the errors between the T–S fuzzy systems and the interpolated systems as feedbacks to ensure that the errors tend to zero. Then, we design stable controllers for the fuzzy control systems based on the obtained systems with piecewise multi-linear interpolations and express our results as a group of linear matrix inequalities. It is proved that when the MFs are both single-variate and multi-variate, our results can stabilize the T–S fuzzy control systems. Finally, several simulation examples are utilized to illustrate the merits of the proposed method with both PDC and non-PDC in this paper.