Active Fault-tolerant Control for Discrete-time Markov Jump LPV Systems via Time-varying Hidden Markov Model Approach

In this paper, the active fault-tolerant control problem is studied for a class of discrete-time Markov jump linear parameter-varying systems. The partial information transmission between the fault diagnosis and isolation scheme and the controller reconfiguration mechanism is characterized by a time-varying hidden Markov model (HMM). The average dwell-time switching signals are employed to describe time-varying characteristics of conditional transition probabilities governing the mode variations of HMM. By using the mode-dependent and parameter-dependent Lyapunov function approach, sufficient conditions are obtained for solving fault estimation and reconfiguration problems, such that the corresponding estimation error and closed-loop systems are input-to-state stable in the stochastic sense. Finally, effectiveness and applicability of the developed approach are validated via two numerical examples.