Finite-Time Stability for Interval Type-2 Fuzzy Nonlinear Systems via an Observer-Based Sliding Mode Control

This work focuses on the design of a sliding mode controller for a class of continuous-time interval type-2 fuzzy-model-based nonlinear systems with unmeasurable state information over a finite-time interval. Aiming at describing the nonlinearities containing parameter uncertainties that inevitably appear in practice, the interval type-2 fuzzy sets are employed to model the studied system. To improve the designing flexibility, a fuzzy observer model non-parallel distribution compensation scheme is designed to estimate the state information of the plant, i.e., the observer is allowed to have a mismatching premise structure from the system. On this basis, the appropriate fuzzy sliding surface and fuzzy controller are constructed by following the same premise variables as the designed fuzzy observer. Then, by means of the sliding mode control theory and the Lyapunov function method, some novel sufficient criteria are established to ensure the finite-time boundedness for the studied systems via a partitioning strategy including the reaching phase, the sliding motion phase and the whole time interval. Furthermore, the designed gains are acquired by solving the matrix convex optimization problem. Finally, the effectiveness of the developed method is demonstrated by two simulation examples.