Dynamic output feedback controller design for interval type-2 T–S fuzzy fractional order systems

This study discusses the issue of the stabilisation of interval type-2 Takagi–Sugeno (T–S) fuzzy fractional order systems by designing the dynamic output feedback controller. In the system model, the system matrix has no assuming limitations. Different membership functions are attached to the T–S fuzzy model and fuzzy controller. For fractional order of 0 < α < 1 case, sufficient conditions in terms of strict linear matrix inequalities are addressed. Then, for 1 < α < 2 order case, by some contragradient transformations, sufficient stability conditions in terms of convex optimisation problems are derived. All of the proposed theorems are strict linear matrix inequalities and can be solved in standard software. Finally, two numerical simulation examples are given to illustrate the effectiveness of the proposed method.