Local stabilization for discrete-time T–S fuzzy time-delay systems with sensor fault

Abstract

This paper focuses on a local stabilization problem for discrete-time T–S fuzzy time-delay systems with sensor fault and external disturbances. The main purpose is to synthesize a controller such that the state can be restricted into a pre-specified region even when the system is subject to sensor fault and external disturbance. First, by restricting the reachable set into an ellipsoid set which is contained in the objective domain, the system state is restricted into the objective area such that the local stabilization can be achieved. Second, the differential mean value theorem is used to determine the bound of the deviation between the membership function of the system and that of the controller. Then, the information of the deviation is employed for designing the controller. Different from some existing methods, in the proposed method, the influence of the sensor fault on the membership function of the controller has been fully considered and the information of aforementioned deviation is made full use of such that a less conservative stability criterion can be derived. Meanwhile, due to the use of the differential mean value theorem, the deviation bound can be calculated. Then, the requirement, where the deviation bound of is assumed to be previously known, is removed. Finally, an example is presented to verify the effectiveness of the proposed method.