Robust H∞ Adaptive Sliding Mode Fault Tolerant Control for T-S Fuzzy Fractional Order Systems With Mismatched Disturbances

This paper deals with the H
_∞
adaptive sliding mode fault tolerant control problem for uncertain Takagi-Sugeno (T-S) fuzzy fractional order systems (FOSs) of fractional order 0 <; α <; 1 with mismatched disturbances. Adaptive laws are designed to estimate the upper bounds of the nonlinear terms. A sliding surface with reduced dimension is constructed by the method of state transformation. A sufficient condition in terms of linear matrix inequalities (LMIs) is established which guarantees the stability of the sliding motion. Then, a new control law is designed to make the resulting control system reach the sliding surface in a finite time. Both state and output feedback control forms are addressed. The proposed methods are illustrated by numerical simulations.