Stability analysis of type-2 fuzzy systems

Type-2 fuzzy systems have successfully been applied in control applications. Due to the complicated structure of type-2 systems, they lack systematic control design and hence the stability of the system is not guaranteed. This paper presents stability analysis of dynamic type-2 Takagi-Sugeno-Kang (TSK) fuzzy systems. Novel inference mechanisms for type-2 TSK systems for the case when antecedents are type-2 and consequents are crisp numbers (A2-C0) are developed and utilized in fuzzy model generation. Owing to the simple nature of the proposed methods, they are easy to implement in real-time applications. One of the proposed inference mechanisms is used and the sufficient stability conditions for these systems are derived. It is shown that the criteria obtained herein must satisfy some linear matrix inequalities (LMI) and an algorithm is also presented to solve the obtained LMI. Two numerical examples are provided that detail the design method. The methodology presented proves to be an efficient approach to systematically design stable dynamic type-2 TSK fuzzy systems.