Dynamic Event-triggered-based Asynchronous Control For Singular Markov Jump Systems

With the continuous deepening and application of modern control theory,singu-lar system has received extensive attention from scholars in recent years since its wide applicability.Due to its outstanding performance in mechanical engineering modeling,electrical circuits and economic systems,some fundamental concepts and numerous re-sults have been successfully generalized from the regular systems to singular systems by scholars,which resulting in many important hybrid systems,singular Markov jump sys-tem is one of them.As a very important type of hybrid dynamic system,it is often applied to describe systems with complex structures and uncertain parameters,and is widely used in circuit systems and network systems.Moreover,neutral systems are widely used in var-ious systems with time delay because they can describe the lags of the system state and state differential simultaneously.Network control systems have been become a hot topic in recent years with the development of network transmission technology and needing of people's normal life.To solve the problems of network delays,packet loss,packet disor-ders and quantization issues over network,triggered scheme was introduced by scholars.On the other hand,cyber-attacks are also a very difficult and urgent problem in the net-work control system,which has very important strategic significance.Based on the dynamic event-triggered strategy,this paper focuses on the control problem of singular Markov jump systems.Singular Markov jump systems and neu-tral singular Markov jump systems are regarded as the research objects,respectively.Combing with the theory of H_? control,passive control,guaranteed cost control,cyber-attacks and deception attacks,three different controllers have been designed by adopting dynamic event-triggered schemes and asynchronous control.This paper mainly studies three issues,they are problem of asynchronous passive dynamic event-triggered controller design for singular Markov jump systems with general transition rates under stochas-tic cyber-attacks,problem of dynamic event-triggered and guaranteed cost asynchronous control for singular Markov jump systems against deception attacks and problem of asyn-chronous H_? controller design for neutral singular Markov jump systems under dynamic event-triggered schemes.Lyapunov functional method and free weight matrix method are mainly used in this paper,and by utilizing some related lemma and definition,some sufficient conditions for stochastic admissible or stochastic stable of the closed-loop sys-tems under the corresponding performance has been given.And in the light of a series of linear matrix inequalities with feasible solution,the asynchronous controller and the dynamic event-triggered rule is designed simultaneously.At last,three sets of numerical instances are offered to reveal the usefulness and effectiveness of the developed method.By the way,the primary contributions of the paper are given below:(1)Based on a singular Markov jump system,a novel resilient asynchronous con-troller is designed by the combination of cyber-attacks and dynamic event-triggered rule.The dynamic event-triggered schemes are extended to the network control systems which cyber-attacks exists,and fairly significant effect is acquired in declining total data trans-mission over the network.(2)Based on a singular Markov jump system and combined with dynamic event-triggered schemes,a resilient asynchronous controller which can against deception attacks is designed.The dynamic event-triggered schemes are adopted to further decrease total data transmission over the network under the circumstances that deception attacks exist.(3)Based on the dynamic event-triggered schemes,an asynchronous controller is designed for a novel system which composed of singular Markov jump systems and neu-tral systems.Some existing application of singular Markov jump system are extended to neutral singular Markov jump systems.