Fault-Estimation and Fault-Tolerant Control for T-S Fuzzy Descriptor Systems With Disturbances

The article investigates the problems of sensor fault estimation and fault-tolerant control for T-S fuzzy descriptor systems with disturbance. A novel regular form is devised for the fault estimation of T-S fuzzy descriptor systems, transforming the systems into a block structure. This transformation not only separates the observable and unobservable parts but also converts the singular matrix of the systems into a symmetric form, thereby simplifying the observer design and eliminating the equality constraint arising from the presence of the singular matrix. Subsequently, a controller in terms of the sliding mode observer is developed. Sufficient conditions are provided by the linear matrix inequality method for achieving simultaneous estimation of sensor faults and system states, as well as ensuring the stability of the overall closed-loop system. Furthermore, the sliding mode input of the sliding mode observer is designed to satisfy the reachability condition. Finally, three simulation examples are provided that illustrate the effectiveness of the proposed results. Note to Practitioners—Safety-critical systems (e.g., aerospace and nuclear power) require that the control systems can handle various abnormal conditions, including failures, loss of control, and equipment damage. The focus of this article is on fault estimation and fault-tolerant control, aiming to ensure acceptable performance and stability levels for safety-critical systems in the event of a fault occurrence. T-S fuzzy descriptor model is considered, T-S fuzzy model can convert intricate nonlinear problems into linear ones, and the descriptor form can encompass a broader spectrum of dynamic models than those of normal systems by taking into account the static constraints among variables. The new regular form proposed in this article ensures the feasibility of the sliding mode observer for T-S descriptor systems, and the method is also suitable for normal systems. Moreover, the reduced-order characteristic of the designed observer is advantageous for increasingly complex industrial systems.