Observer-based H∞H∞ controller design for interval type-2 T–S fuzzy systems

This paper focuses on studying observer-based controller synthesis for nonlinear plant subject to parameter uncertainties, which is represented as interval type-2 T–S fuzzy model. An interval type-2 fuzzy augmented system is formed by an interval type-2 T–S fuzzy model, an interval type-2 fuzzy observer and an interval type-2 fuzzy controller connected in a closed loop. Based on the Lyapunov stability theory, the stability of the interval type-2 fuzzy augmented systems is investigated. Some matrix inequality techniques are applied to derive stability conditions in the form of linear matrix inequalities (LMIs). With the consideration of the information of lower and upper membership functions, more relaxed stability conditions are obtained to guarantee the system stability. Finally, two numerical example are provided to illustrate the effectiveness of the proposed conditions.