Observer‐based sliding mode fault tolerant control for nonlinear descriptor systems

In this article, the design and analysis of fault tolerant control (FTC) are investigated for stochastic nonlinear descriptor systems by using the sliding mode approach. First, an integral sliding mode‐based descriptor observer (ISM‐DO) is constructed to estimate the state and fault. The proposed ISM‐DO retains the basic characteristics of descriptor systems, meanwhile, it is not only suitable for dual normalized descriptor systems, but also for non‐dual normalized descriptor systems. It is more universal than the existing sliding mode fault tolerant control (SMFTC) methods. In the sequel, a novel restricted equivalent form based algorithm is developed to solve the sliding parameters. The proposed method provides a general algorithm, and it does not impose additional rank constraints. Further, a new adaptive sliding mode fault tolerant controller is constructed to stabilize the fault system, the assumption related to the diffusion matrix is removed. Based on these ingredients, the asymptotically mean square admissibility of the closed‐loop fault system and the observer gain matrix are got by a sufficient linear matrix inequality condition. The effectiveness of the proposed method is verified by simulations.