Observer-based H_∞Robust Fault Detection For Markov Jump Systems

The main purpose of this thesis is to design a novel fault detector based on proportional integral observer for singular Markov jump systems. The considered fault signals and disturbances can be unbounded, just with one of their higher derivatives bounded. A proper observation model, which makes the residual signal satisfy a certain performance indicator, is established, in order to ensure the system to work normally under inevitable disturbances and noises, while raise an alarm when a fault occurs.Firstly, a new formulation of the bounded real lemma (BRL) for singular linear Markov jump systems is given, which ensures the considered systems to be stochastically stable and robust to unknown input via LMI approach. Through an augmented system, the designed PI observer can estimate the system state, fault and disturbance vectors together with their finite time derivatives simultaneously. Moreover, by choosing proper integral gain, the sensitivity to fault signal is increased, while the influence of disturbance from environment changes, modeling error, etc. can be reduced. Theorems are given and proved to be right to guarantee the observer to be regular, impulsive free and strong observable just as the original system. Then the design of observer-based residual generator may come down to filtering problems under random abrupt. The residual signal is filtered to satisfy the performance index, and sufficient condition is derived through the improved BRL. Also, on this basis, an appropriate residual function and threshold are set up to evaluate the residual error. The failure criteria are given to ensure the function to be less than the threshold in fault free condition, which means the system can work normally under disturbance, while greater than the threshold when fault occurs, which means the system will raise an alarm automatically. A numerical example is then presented to verify the effectiveness of the given result.Next, a PI observer is settled for time-delay Markov jump systems, and similar technique for linear system is applied to obtain a sufficient condition which ensures the observer to be regular, impulsive free, strong observable, and stochastically stable, while the residual signal to satisfy the given H∞performance index. Finally, by using LMI toolbox in MATLAB, a numerical example is given to verify the effectiveness of the conclusion.At last, a summary of this paper is given. At the same time, we give an expectation for the future work.