Stability Analysis And Sampling Control Of Hidden Semi-Markov Jump Systems

In the past few decades,the stability of Markov jump systems has been studied widely.However,the application of Markov chain is limited to the sojourn time satisfying memory-free distribution(discrete time sojourn time of Markov chain satisfying geometric distribution,continuous time sojourn time of Markov chain satisfying exponential distribution),which is difficult to achieve in practice.Semimarkov chain is a natural extension of Markov chain.The sojourn time of semiMarkov chain can satisfy any distribution.Therefore,the application scope of semi-Markov jump system is wider than that of Markov jump system.In many studies of Markov jump systems and semi-Markov jump systems,it is always assumed that the system mode is completely known.However,there are many practical systems that cannot satisfy this condition,such as time-varying delay and packet loss models.Hidden semi-Markov chain is proposed to study this kind of problem and has been studied a lot.Hidden semi-Markov chain is a double stochastic process and an extension of semi-Markov chain.Hidden semi-Markov model contains a bottom layer and an observation layer.The bottom layer is a hidden semi-Markov chain whose state sequence is not observable,so it is called hidden,while the observable layer is an observable mode sequence,from the bottom layer to the observable layer there is emission probability.So it is necessary to study the hidden semi-Markov jump system.Based on the existing research at home and abroad,the stability analysis and controller of semi-Markov jump system and hidden semi-Markov jump system are carried out in this thesis.The main research content of this thesis is divided into the following three aspects:Firstly,the stability analysis and controller design of hidden semi-Markov jump systems are studied.Considering the influence of transition probability and sojourn time on the stability of the system,a new criterion for the -error mean square stability of semi-Markov jump systems is established by constructing multiple Lyapunov functions,and a stability controller dependent on the observation mode and sojourn time is constructed.Finally,an example is given to illustrate the validity of the results obtained.This result generalizes the existing semi-Markov jump system which only considers the sojourn time effect on the stability.Secondly,the stability analysis and controller design of no-homogeneous implicit semi-Markov jump systems with limited transition probability are studied.During the operation of the system,if the real mode of the system does not match the observed mode,the controller can make the system stable by transition probability.By constructing multiple Lyapunov functions that depend on both the current system mode and the sojourn time of the system in the current mode,the influence of transition probability and sojourn time on the mean square stability of implicit semi-Markov jump systems is discussed.Finally,an example is given to illustrate the validity of the results obtained.This result generalizes the existing results which assume that the transition probability is completely known.Thirdly,the passive control of complex-valued neural networks is studied.Considering the complex value random reaction-diffusion memristor neural network model,two new sampling control methods,including spatial sampling and time point sampling,are used to obtain more accurate sampling methods.Finally,examples are given to illustrate the validity of the conclusions obtained.This result generalizes that only time point sampling is considered in real-valued neural network model sampling.