Dynamic Output Feedback Controller Design for Uncertain Takagi–Sugeno Fuzzy Systems: A Premise Variable Selection Approach

This article presents new design conditions of full-order dynamic output feedback controllers for continuous-time Takagi-Sugeno (T-S) fuzzy systems allowing the selection of premise variables to be used in the control law. The fuzzy output controller is allowed to have a different number of fuzzy rules and a different set of membership functions from the T-S model. This includes the cases of complete or partial immeasurable premise variables. The main aspect of the proposed methodology is to present conditions such that the control gains are independent of the premise variables that cannot be measured allowing flexibility for the designer in a realistic output feedback context. For this purpose, the design conditions are expressed as linear matrix inequality relaxations combined with scalar parameters that provide extra degrees of freedom. The proposed control methodology also deals with model uncertainties and the use of fuzzy Lyapunov functions. The effectiveness and applicability of the methodology are shown through numerical examples.