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.

I. Introduction

When building mathematical models for physical or man-made systems, switched systems can be used because of the switching features of the practical systems, for instance, power electronics, network control models, tunnel diode circuit system models, flight control models, and induction motor systems [1]. In [2], quantized control was explored for a cluster of networked switched systems under the round-robin protocol and was applied to two inverted pendulums. In [3], the issue of global stabilization was investigated for switched feedforward time delayed systems where time delays appeared in states, as well as inputs and a practical switched induction heater circuit system was studied. Sun et al. [4] focused on the fault detection issue for switched models and a typical switched radio link control circuit was used to show the utility of the developed parity space-based fault detection method. In [5], the event-triggered multisource bumpless transfer control problem of networked switched systems with the almost output regulation performance subject to switching deception attacks was investigated, and a switched resistance–inductor–capacitance circuit was researched. However, there are still many stability analysis issues that need to be addressed for switched systems, such as switched systems with faults, switched systems with delays, and so on, which arouses our great research interest.