Analysis And Control Of Markov Jump Systems With Event-Triggered Scheme And Quantization

With the widespread use of computer network and the continuous development of micro-electronic technology,in recent years,networked control systems appear with a wide range of control model distributed.Due to the involvement of communication network,some problems occur inevitably,such as networked delay,data packet dropout,packet disorder,which may reduce systems' performance,even make systems unstable.The main reasons of these problems are owing to the limited networked bandwidth.The introduction of quantizer in networked control systems greatly improves the capacity of data transmission,and many relevant literatures have been published,most of them adopt periodic sample scheme.However,this method will send unnecessary control information,which will occupy network resources.To solve this problem,the researchers propose a new mechanism called event-trigger scheme,which has aroused wide concern because it can reduce the frequency of control task effectively.However,there are few papers considering quantification and event trigger scheme at the same time.On the other hand,Markov jump modeling presents in many practical systems.It is significant to study networked control systems with Markov jump model.According to the above analysis,based on event-triggered scheme,this paper will use logarithmic quantizer to investigate H_? control problem,H_? filter problem and guaranteed cost control.Here are the main objectives:1.In the case of existing delays and quantizations in both sensor-control channel and control-actuator,based on event-triggered scheme,the quantized control for Markov jump system is investigated.In order to reduce the transmission of invalid data,firstly,an event generator is introduced into the state feedback channel,the data is send to the quantizer after being filtered by the event generator.Considering the network time delay,taking time-delay system method,the interval [8),] is divided into N sub-regions,then the mathematical model of closed loop system is established.Constructing the Lyapunov function,to deal with the cross terms by using of free-weighting matrix approach in order to reduce the conservative.,the obtained stability condition satisfy the H_? performance index,and how to design the H_? controller is discussed.Finally,the effectiveness of the control algorithm is verified by a numerical example.2.The problem of quantized event-triggered H_? filtering for Markov jump systems is investigated.Firstly,in order to reduce the waste of communication resources an event-trigged scheme is given.Taking the time-delay system method,the model of filter error system is build,which includes delay,quantization and event-trigger parameters.Based on the new Markov jump system,constructing the Lyapunov functional,using the interactive convex combination method instead of the free weight matrix method to reduce the complex computing.,the stability condition are satisfied with H_? performance index,based on which the H_? filter parameters are designed.Finally,the influence of quantization density on the maximum time delay is analyzed.3.By introducing an event generator into the sampler,the problem of event-based quantized guaranteed cost control for Markov jump systems is investigated.In order to save network resources,the state feedback signals and the control input signals are encoded by two logarithmic quantizers,and the closed loop event-trigger control system is transformed into an equivalent time-delay system with the sector bounded method.Considering the effect of double channel delay,by constructing the Lyapunov-Krasovskii function.the system stability condition is obtained described by a set of linear matrix inequalities.Furthermore,the controller is designed to ensure the stability of the system while satisfying the given guaranteed value.