Tracking Control for Nonlinear Systems With Actuator Saturation via Interval Type-2 T-S Fuzzy Framework

In this work, the problem of tracking control for discrete-time nonlinear actuator-saturated systems via interval type-2 (IT2) T-S fuzzy framework is investigated. Improved on the (type-1) T-S fuzzy system, the IT2 T-S fuzzy system has a better capability for the expression of system uncertainty, and correspondingly, it will increase the difficulty of analysis, especially for the membership-functions-dependent (MFD) method. In addition, in this case, the control input nonlinearity caused by actuator saturation will complicate the stability analysis of the systems. We make an attempt to address the challenges that the information of membership functions (MFs) is underutilized or not utilized, by developing an MFD analysis approach, which allows the enhancement of design flexibility of IT2 fuzzy controller and effectiveness of lessening the conservativeness of the analysis result. The piecewise MFs which are formed by connecting the sample point on or close to the original IT2 MFs are utilized to approximate the original IT2 MFs, and the error between the piecewise MFs and the original upper and lower MFs is taken into account in the stability analysis. To acquire the linear matrix inequality-based (LMI-based) constraint, the actuator saturation is converted to a sector nonlinear issue. ${H}_{infinity}$ performance is considered to limit the difference between the reference system and the control saturated system. Examples are presented to illustrate the validity of the results.