Finite-Time Control for Multiple Time Delayed Switched Random Systems via a k-Step Fault Estimation Technique

This article focuses on the finite-time fault estimation observer and controller design for switched random models subject to multiple time-varying delays. It is assumed that there exist actuator faults, model nonlinearities, external disturbances, and sensor faults in these systems. First, an observer is proposed to obtain the estimations of the system states, disturbances, as well as sensor and actuator faults. Compared with the existing results, the suggested observer estimates these sizes and shapes of states, exogenous disturbances, actuator, and sensor faults more accurately. This kind of unknown nonlinear dynamic can be approached by this generalized fuzzy hyperbolic model. Delay-dependent sufficient conditions of robust mean-square finite-time boundedness are obtained for the error system via a piecewise Lyapunov function. Observer matrices are obtained and finite-time fault estimation is realized. Second, we establish a novel controller based on fault estimation information. In addition, the piecewise function is developed to acquire delay-dependent adequate conditions of finite-time control. Controller matrices are obtained and finite-time fault-tolerant control can be achieved. At last, this validity of the method shown in this work is demonstrated via a practical simulation example.