Robust $$H_{\infty }$$ adaptive output feedback sliding mode control for interval type-2 fuzzy fractional-order systems with actuator faults

This paper addresses the $$H_{\infty }$$ adaptive output feedback sliding mode fault-tolerant control problem for uncertain nonlinear fractional-order $$\hbox {systems}$$ (FOSs) with $$0<\alpha <1$$ . The interval type-2 Takagi–Sugeno model is employed to represent the FOSs. Adaptive laws are designed to estimate the upper bounds of the nonlinear terms and mismatched disturbances. A reduced dimension sliding surface is constructed based on system output. A sufficient condition is established in terms of linear matrix inequalities to guarantee the stability of the sliding mode. Then, a control scheme based on fractional-order reaching law is proposed to make the resulting control system reach the sliding mode surface in a finite time. The effectiveness of proposed methods is illustrated by a numerical simulation example.