Asynchronous Synthesis For Markov Jump Systems

Markov jump system,as a special kind of hybrid system,is favored by scholars in both academia and industry because of its simple mathematical description and powerful modeling ability.It has been widely applied in power systems,aerospace systems and many other engineering fields.In the study of Markov jump system,using hidden-Markov-model based method to deal with asynchronous issues can effectively overcome the difficulty of obtaining accurate modes in the practical systems,and also can reduce conservatism by making full use of available mode information.Therefore,it is significant to study the asynchronous synthesis of Markov jump system based on hidden Markov model from both theoretical and practical point of view.Based on hidden Markov model,this paper investigates the asynchronous synthesis problems for several types of Markov jump systems.The considered issues include control,filtering,model order reduction,and fault detection.The main contributions of this paper are summarized as follows:(1)An asynchronous filter is designed for periodic Markov jump system,which has the same periodicity as the considered periodic system.Firstly,the exponential mean square stability and strict dissipativity of the filtering error system are analyzed based on Lyapunov method,and then sufficient conditions are given in the form of matrix inequalities.An extra matrix is introduced to make the matrix inequalities be in a concise form.Furthermore,the design method of the filter parameters is proposed by means of slack matrix technique and Projection lemma(2)The issue of asynchronous model reduction is investigated for Markov jump sys-tems.Since the probability information in the practical systems can not be obtained accu-rately,we consider the transition probability matrix in a polytopic structure and the condi-tional probability matrix with partially known entries.Based on H∞ theory and Lyapunov method,the design method of the asynchronous reduced-order model is presented.(3)An asynchronous quantized state feedback controller is designed for Markov jump time-delay systems.Since there is bandwidth constraint in the transmission channel,a mode-dependent logarithmic quantizer is introduced.The system,filter and quantizer are piecewise asynchronous,and the asynchronous relationships are described by two hidden Markov models respectively.The upper and lower bounds of time delay are fully used to design the asynchronous controller.The proposed controller can ensure that the closed-loop system is stochastically mean-square stable and has a prescribed H∞ noise attenuation performance.(4)The asynchronous filtering problem is considered for Markov jump neural net-works.Similarly as(3),a mode-dependent and asynchronous logarithmic quantizer is in-troduced to reduce the data transmission rate.Based on the Lyapunov functional method and scaling techniques,an asynchronous filter is designed,which can ensure the filtering error dynamics is stochastically mean square stable and strictly dissipative.The design method takes the upper and lower bounds of time delay and the characteristics of nonlinear term into consideration.(5)Asynchronous controller and filter are designed for two-dimensional(2-D)Bernoul-li jump systems.Firstly,the asymptotic mean square stability and H2 performance of the 2-D hidden Bernoulli jump system are analyzed,and sufficient conditions are derived based on Lyapunov method.Since the corresponding closed-loop control system and filtering er-ror system have the characteristics of 2-D hidden Bernoulli jump system,asynchronous controller and asynchronous filter for 2-D Bernoulli jump system are designed based on the above sufficient conditions(6)An asynchronous fault detection scheme is proposed for 2-D Markov jump sys-tems.An asynchronous 2-D fault detection filter is designed to generate a residual signal to indicate whether a fault occurs or not in the system.If the value of the residual function is greater than the threshold,it indicates that a fault occurs;otherwise,there is no fault.Ad-ditionally,the transmission probability matrix and conditional probability matrix are only partially known.The designed fault detection filter is proposed such that the overall fault detection system asymptotically mean square stable and strictly dissipative.