Extended Dissipative Interval Type-2 Fuzzy Sampled-Data Tracking Control for Uncertain Nonlinear Systems

The mathematical models of systems within a wide range of domains possess notable nonlinearity and uncertainty, posing significant constraints on the analysis and synthesis of these systems. In particular, it is noteworthy that these system features make efficient control extremely difficult. On the other hand, a thorough analysis with corresponding constraints on the dissipativity of the controller can enhance its control performance. However, for complex nonlinear systems, analyzing multiple types of dissipativity is quite arduous, while conclusions drawn from the analysis of a single type of dissipativity lack generality, resulting in limited applicability. In view of the above, the sampled-data tracking control for systems with nonlinearities and uncertainties is investigated in this work. The uncertainty and nonlinearity of the system are captured by the interval type 2 (IT2) fuzzy framework. For achieving exceptional flexible design and performance requirements, the extended dissipativity analysis of sampled-data IT2 fuzzy tracking system is innovatively presented. To reduce the difficulty encountered in realizing the fuzzy controllers, a mismatched premise information design is introduced into the controller structure. Additionally, an innovative membership function-dependent (MFD) technique, grounded in piecewise linear membership function (PLMF), is utilized within the framework of extended dissipativity analysis and controller design. This technique facilitates a more comprehensive exploitation of the information in the membership functions (MFs), effectively reducing conservativeness in the proposed conditions and enhancing controller performance. Finally, numerical examples are exhibited, proving the efficacy of the designed method.