H_? Filtering For Markov Jump Systems With Partly Unknown Transition Probabilities Based On Delta Operator

Networked Control Systems(NCSs)have received researches and attention from a large number of scholars because of their flexible using,convenient maintenance,and low costs.NCSs are composed of sensors,communication networks,controllers,and actuators.Due to the introduction of the network,some unstable factors such as random delays,data losses,etc.will appear in the system.The factors such as packet losses and time-delays will lead to poor transient response of the system.The Markov jump systems that with limited operating modes are special kinds of hybrid systems.The mode transition process in the Markov jump systems has a memoryless nature,that is,the previous mode and the mode at the next moment which obeys the system transition probabilities in the time series are independent of each other.However,it is difficult to accurately obtain the system modes transition probabilities in the actual Network Control Systems.Therefore,the Markov jump systems with unknown transition probabilities are more in line with the actual indus-trial control systems.Under high-speed sampling,the shift operator cannot simulate the original con-tinuous-time system response well.In contrast,the Delta operator which make the system responses infinitely close to the continuous-time system under discrete time conditions can better restore the original continuous-time system responses under high-speed sampling.This thesis using the Delta operator discretization method to construct the Mar-kov jump systems model with partly unknown transition probabilities researches a type of H_? filtering problem under the conditions of packet losses,uncertain system parameters and random time-delays.The research results include the following as-pects:(1)The Delta operator discretization method is used to construct the Markov jump systems model with partly unknown transition probabilities and the filtering er-ror system.The Lyapunov function and the Linear Matrix Inequality(LMI)are not only used to analyze the stability of the system,but also obtained the parameters of the mode-dependent filter.The numerical simulation compares the results obtained by using the shift operator and the Delta operator that prove the superiority of the Delta operator discretization method.(2)Investigate the robust H_? filtering problem under the conditions of packet losses for Markov jump systems with partly unknown transition probabilities.As-suming that the system packet losses probability obeys Bernoulli distribution,a Mar-kov jump system with uncertain parameters is constructed based on the Delta operator.Lyapunov function and Schur complement lemma are used to obtain sufficient condi-tions for the stochastic stability of the system.The numerical simulation part proves the system performance using the Delta operator discretization method is better than the shift operator discretization method under the same packet losses rate.The result of filtering error response proves the effectiveness of the method proposed in this part.(3)Research the H_? filtering problem of Markov jump systems with random one-step delays and partly unknown transition probabilities.It is assumed that the random one-step delays occur between the system sensors and the filter as well as the probability obeys the Bernoulli distribution.Based on the Delta operator,the Markov jump systems with partly unknown transition probabilities is constructed.Using the Lyapunov function and the LMI method designs the mode-dependent filter and ac-quires its parameters.The numerical simulation not only proves the effectiveness of the method proposed in this part,but also indicates that the system with a certain probability of random one-step delays is still stochastically stable and satisfies the given H_? performance.