Fault Detection For Descriptor Markovian Jump Linear Systems

Recently, increasing emphasis on safty and reliability has been witnessed in manufacturing and control systems, which has also given a decisive impulse for the process of model-based fault detection and isolation(FDI) technology. In the meantime, singular systems and Markovian jump linear systems(MJLSs) have also been extensively studied owing to their great capability of system modeling. The attention in this dissertation is focused on fault modeling and fault detection for continuous descriptor MJLSs. The main contributions of this thesis are as follows:First of all, the faulty model of descriptor MJLSs is established, and then the advantages of state-space description in time domain over the transfer function description in frequency domain are pointed out.Secondly, the generalized bounded real lemma and its deduction for descriptor MJLSs are presented and proved, after introducing the definitions of regularity, impulse elimination and stochastical stability. The performance requirements for robustness and sensitivity of fault detection system are formulated into two L2-induced gain constraints. Then, a sufficient condition for the existence of the desired fault detection filter is obtained. Moreover, an iterative linear matrix inequality(LMI) algorithm for computing the desied filter parameters is shown. In addition, the residual evaluation method is given.Thirdly, the robust fault detection issue for descriptor MJLSs is investigated. The common existence of uncertainties and time delays in modern control systems is discussed, and the assumptions for time-varing parameter uncertainties and time-varing state delays in this thesis are presented. Afterwards, two preliminary theorems aiming at robustness and sensitivity analysis are proved, and a sufficient condition for the existence of the desired robust fault detection filter, an iterative LMI algorithm as well as the adaptive residual evaluation strategy are given, respectively.Finally, the corresponding numerical simulation illustrates the applicability and effectiveness of the proposed techniques.