Non-fragile sliding mode observer based fault estimation for interval type-2 fuzzy singular fractional order systems

In this paper, an interval type-2 fuzzy model is presented to describe the nonlinear singular frac-tional order systems (SFOSs) with 0 < alpha < 2. The problem of actuator and sensor fault estimation is addressed by designing a non-fragile sliding mode observer (SMO). Firstly, a new criterion is provided to analyse the admissibility of SFOSs, which does not need to divide the fractional order interval (0, 2) into interval (0,1) and interval [1, 2) to study them separately. Then, by expanding the dimension of the SFOS, the non-fragile SMO and the sliding surface are constructed and the accurate estimations of faults and the SFOS state simultaneously are achieved. A new reaching law is designed, which can divide the process of the system moving to the sliding surface into three stages. Further the con-trol law is constructed to guarantee the observation error reaches the sliding surface in finite time. Finally, three examples show the effectiveness of the proposed scheme.