Finite-time Filtering For Discrete-time Singular Markov Jump Systems

In actual production activities,we often encounter some similar situations,such as the car breaks down,the phone shut down for no reason,the machine suddenly stops working and so on.Most of these cases are failures in some parts of the machine,resulting in changes between the subsystems are connected,which changes the structure and parameters of the whole systems.If a system like this,we can use the Markovian jump systems to describe it.But with the development of the science and society,people have a higher request for production tools,only considering the Markovian jump systems model can not enough to deal with complex production needs,so the discrete-time singular Markovian jump systems arises at the historic moment.The system can more precisely describe the controlled object,so it has been attracted the attention of many research scholars.This paper research is based on the problem of finite-time filtering for discrete-time singular Markovian jump systems.The paper,by constructing suitable Lyapunov function,selecting new lemma and def-inition,using linear matrix inequalities(LMIs),convex optimization method,a sufficient condition is firstly established such that the filtering error systems to be finite-time bound-edness.The specific work is as follows:(1)Finite-time H_? filtering for the discrete-time singular Markovian jump systems with partially unknown transition probabilities has been studied,and the problem of time-varying delay and actuator saturation have also been considered.The known and unknown parts of the transition probabilities were discussed separately,adopting a similar method to obtain a sufficient condition for finite-time boundedness for the error systems.(2)The paper discussed the finite-time dissipative problem for discrete-time singular Markovian systems with uncertainties.In the same way,the proper Lyapunov function has been constructed and the new lemmas were introduced to deal with the uncertainties.Fi-nally,the determination of finite-time dissipation was obtained by using the linear matrix inequalities method.(3)The paper discussed the problem of finite-time non-fragile control based on H_? filtering for discrete-time singular Markovian jump systems.Moreover,the nonlinear sys-tems also has been considered,which makes the model of the system closer to the real life.The suitable Lyapunov function and difference inequality were constructed,and obtained the finite-time bounded conditions and the gain matrix of the filtering error systems.