Event-triggered Control And Filtering For T-S Fuzzy Singular Semi-Markov Jump Systems Against Multiple Cyber-attacks

Markov jump systems can be regarded as the sequential connection of several deterministic subsystems in different time fragments,in which the switch law of each subsystem is determined by the Markov chain.It can effectively describe the abrupt changes of system structure or parameters,so it is more suitable for modeling real systems with random characteristics.In fact,compared with Markov jump systems,semi-Markov jump systems have wider applications for physical systems because their sojourn time satisfies more general distributions,such as the Gaussian distribution,the Weber distribution,etc.Singular systems are described by a series of differential and algebraic equations,also known as generalized systems or differential algebraic systems.Compared with regular systems,singular systems can describe the whole feature of physical systems more accurately,which include both dynamic and static characteristics of physical systems.When the coefficient matrix of the singular system satisfies the random property of the semi-Markov process,singular semi-Markov jump systems are produced.Cyber-Physical Systems(CPSs)are intelligent systems that integrate physical processes,ubiquitous computing,efficient communication,and effective control,which can greatly improve the performance of physical systems.As a special kind of CPS,singular semi-Markov jump CPSs are widely used in various fields,but they still face many challenges.On the one hand,a large number of components are connected through communication networks,which makes it important to improve the efficiency of communication.Therefore,eventtriggered schemes are proposed to further improve the communication efficiency for actual systems.On the other hand,the gradual expansion of actual system scale leads to increasingly serious security problems,which result in the urgent study for CPSs against cyber-attacks.In this paper,the event-triggered control and filtering of T-S fuzzy singular semiMarkov jump systems under multiple cyber-attacks are studied.The T-S fuzzy model is used to describe a class nonlinear singular semi-Markov jump system.A DynamicMemory Event-Triggered(DMET)scheme is proposed to improve the communication efficiency for the system.A unified framework of multiple cyber-attacks,including Denial of Service(DoS)attacks and deception attacks,is constructed to improve the security and resilience of the system.Based on the Hidden Markov Model(HMM)to describe the asynchronous phenomenon between the physical process and the controller or filter,the asynchronous security controller and asynchronous dissipative filter with partial known conditional probabilities are designed,respectively.By using the free weighting matrix and Lyapunov-functional method,the stability and admissibility criteria of the closed-loop system or the filter error system are obtained,and the dissipation performance is satisfied.In the light of Linear Matrix Inequalities(LMIs),a co-design method of controller and filter based on the DMET scheme under multiple cyber-attacks is finally obtained.