Finite-time H∞ fault-tolerant control for semi-Markov jump systems with multiple faults: An intermediate variable observer approach

The purpose of this study aims to investigate the finite-time fault-tolerant control (FTC) problem for a type of semi-Markov jump systems(S-MJss) with multiple failures, in which sensor and actuator failures, a nonlinear term and external disturbance are considered. Firstly, a multi-fault observer based on an intermediate variable is designed by coordinate transformation, and the sensor and actuator failures and system state information are estimated simultaneously. In addition, to enhance design flexibility, a term for estimating output error feedback is incorporated into the observer. Secondly, based on the data derived from the aforementioned estimation, an observer-based fault-tolerant controller is introduced to mitigate the effect of failures. To depict the asynchronous phenomenon (AP) concerning the modes of the controller and system, a pattern detection method based on the hidden semi-Markov model (HSM) is utilized. Moreover, the control strategy put forward not just guarantees the stochastic finite-time boundedness (SFTB) of the closed-loop system, but achieves the desired H∞ performance. Finally, the efficacy of the introduced strategy is verified through two simulation examples and a comparison example.