Sensor fault detection and isolation for asynchronous switched systems using a bank of sliding mode observers

This paper studies sensor fault detection and isolation in continuous-time switched systems subject to unknown but bounded output or measurement disturbances. The proposed approach utilizes the asynchronous switching phenomenon, in which there is a lag between subsystem and observer switching. The aim is to design a bank of sliding mode observers for fault isolation, with robustness to residual provided by H∞ performance. For this purpose, we first transform the sensor faults into pseudo-actuator faults using a coordinate transformation with a low-pass filter, making the design of the observer framework more convenient. Then, a series of sliding mode observers is designed for effective fault isolation such that each residual signal is affected by its corresponding sensor fault. Next, to provide an optimal solution in the sense that the effect of measurement disturbances on the residual signal is minimized, the H∞ optimization index is utilized for the problem of asynchronous switched systems. To ensure stability, a piecewise Lyapunov function along with an average dwell time switching constraint is utilized for both matched and mismatched periods of asynchronous switching. The conditions for a feasible solution lead to sufficient conditions that are formulated in terms of linear matrix inequalities. Moreover, the evaluation of the residual signal and threshold is computed to enhance fault detection and isolation capability. Simulations of a three-tank system for multiple sensor faults are utilized to demonstrate the effectiveness of the proposed approach.