LMI-based stability conditions for interval type-2 fuzzy-model-based control systems

This paper investigates the stability of the interval type-2 (IT2) fuzzy-model-based (FMB) control systems. An IT2 T-S fuzzy model is developed to represent the nonlinear plant subject to parameter uncertainties, which are captured by the lower and upper membership functions. An IT2 fuzzy model is then be proposed to close the feedback loop. It is not required that the IT2 fuzzy controller shares the same premise membership functions or the same number of fuzzy rules as those of the IT2 T-S fuzzy model. Consequently, it offers a greater design flexibility to the IT2 fuzzy controllers. However, the mismatched premise membership functions are not favourable to the development of stability conditions and thus leads to a conservative stability analysis result. In this paper, with the consideration of the lower and upper membership functions, which carry the information of the nonlinearities and parameter uncertainties of the nonlinear plant, the stability of the IT2 FMB control systems is investigated based on the Lyapunov stability theory. Stability conditions in terms of linear matrix inequalities are developed to guarantee the stability of the IT2 FMB control systems and synthesize the IT2 fuzzy controller. A simulation example is given to demonstrates the effectiveness of the proposed approach.