The Study On Fault Detection Problem Of Semi-Markovian Jump Systems

In the realistic system,the parameters and the structures of the system are always changed.Semi-Markovian jump systems(S-MJSs)model can describe the system with this kind of property and has aroused considerable attention.Such jump systems are a class of hybrid systems,which is usually consisted of continuous-time S-MJSs and discrete-time S-MJSs.During the past decades,many important results on S-MJSs have been studied,including stability analysis,robust stabilization,input/output feedback control,filter design,state/fault estimation,and fault tolerant control,etc.The sojourn-time of S-MJSs obeys more general distribution,for example,the Wei-bull distribution which relaxes the condition of sojourn-time probability distribution compared with MJSs.Obviously,the difference between the two cases makes the S-MJSs more practical and less conservative.In addition,systems faults and external disturbances always exist in a sea of real systems unavoidably,which may lead to the instability of the control plant and even deteriorate the system performance.Therefore,fault detection of system is particularly important.Motivated by the above discussions,this paper studies the following contents for fault detection problem for S-MJSs:By using filtering method and considering the unknown disturbance signal existing in the system,the fault detection problem for the continuous-time S-MJSs is addressed,where the mode-dependent filter can guarantee that the fault detection system is stochastically stable and satisfies the H_? performance.Here,we use the decoupling method to solve the filter parameters.Based on the continuous-time S-MJSs and in view of the influences of the parameter uncertainty matrix and generally uncertain transition rates,the problem of fault detection and isolation is solved by using geometric method,where the residual generator can make that each fault signal is only affected by the current fault signal and decouples other fault signals.In consideration of the partly unknown transition rates,the fault estimation problem for continuous-time nonlinear S-MJSs is tackled by designing an intermediate estimator,where the constructed error system is bounded in probability based on the system model and the intermediate estimator.Finally,some numerical examples are given to verify the effectiveness of the method for the fault detection problem for the continuous-time S-MJSs.The simulation example of the F-404 engine system are presented to ensure the usefulness of the fault detection based on the geometric method.