Robust Control For Switched Linear Systems With Event-Triggering Scheme

Switched system is a kind of important hybrid system consisting of finite sub-systems(or modes)and a switching signal which decides the working order of the sub-systems.Since switched system can describe many physical systems,it has a wide range of applications.In the control field,the switched system stability has been a hot issue for decades,and quite a few results have been presented.On the other hand,in sampling control system,the contradiction between limited communication resources and complicated control tasks is increasingly highlighted.Thus,in contrast to the traditional time-triggering mechanism(periodic sampling),a new triggering mechanism which depends on the system performance,i.e.event-triggering mechanism,is proposed.Since event-triggering scheme can ensure the desired control performance as well as reduce the communication frequency to some extent,the control system resources are allocated more reasonably.This has received wide attention of academia and engineering applications.Currently,event-triggering scheme has been applied to a variety of systems,e.g.multi-agent systems,networked control systems and random stochastic systems,and lots of valuable research results have been obtained.However,the problem of event-triggered control for switched system has not yet been given enough attention in the control field.In this thesis,the event-triggering scheme is introduced into switched linear system.Moreover,considering that time-delay,disturbance and uncertainty widely exist in practical system,the event-triggered robust control problem is investigated for switched linear system.First,single and multiple continuous event-triggering schemes are respectively studied.This part lays the theoretical and methodological basis for the whole thesis.Second,as the difficulty to continuously monitor the even-triggering conditions in practice,the self-triggering scheme and its control problem are further studied.Furthermore,when the system contains disturbance and time-delay,the Zeno frequent sampling and communication phenomenon is easy to appear if the continuous event-triggering mechanism is adopted.Therefore,the thesis continues to study the multiple discrete event-triggering schemes and the corresponding control problem.Besides,due to the use of switched multiple event-triggering structure,the working order of sub-system,event-triggering scheme and sub-controller is difficult to achieve synchronization accurately.Thus,the thesis investigates the asynchronous robust control for switched system based on the multiple discrete event-triggering scheme.As to the specific arrangement of the study,the full state feedback controllers are used for the control design.As to the stability analysis methods,the multiple Lyapunov functions,and the switching laws based on system state and average dwell time are utilized.In particular,the coupling effect of switching signal and triggering signal on the system performance analysis is throughly clarified.The effect of the both signals on the Zeno analysis is discussed.Moreover,the relationship between transmission delay and sampling period in the networked switched system is studied.Also,the asynchronous control problem among sub-system,event-triggering scheme and sub-controller is investigated.In addition,a term with exponential decay form and a disturbance related parameter is introduced into the event-triggering schemes,by which the triggering frequency is further reduced.Finally,the effectiveness of all the proposed theoretical methods is verified by numerical simulations.