Controllability And Stability Of The Multi-rate NCS

Networked Control Systems (NCS) has gradually become a popular research field in thecontrol theory since the concept of it was defined. With the wide application of NCS, a lot ofproblems and challenges were appeared in control. Recently, the results of NCS research wereobtained almost under the suppose that the node has the same sampling rate. But, in fact, thesampling rate of each node was actually different from each other or not completely the samein application systems. So the concept of multi-rate NCS was suggested in order to describethe NCS more accurately, and solve the problems which appeared in actual application moreeffectively.Firstly, the model of multi-rate networked control systems with both network-induceddelay and packet drop was set up in this paper. It can be formulated as a discrete-timeswitched linear system. The controllability of the model was analyzed according to relevantcontrollability theory of switch system. The related conclusions about controllability of thismodel were obtained. An illustrative example is provided to demonstrate the effectiveness ofthe proposed method.Secondly, the stability of the model was analyzed based on the Lyapunov method. Thesufficient and necessary conditions of asymptotically stable for the models were obtainedaccording to some characteristics of the stability analysis for switched system. An illustrativeexample is provided to demonstrate the effectiveness of the proposed method.At last, the necessary and sufficient conditions of exponential stability for the modelwere obtained using the method of average dwell time for each subsystem. The stabilitycontroller about exponential stability for the model was designed. An illustrative example isprovided to demonstrate the effectiveness of the proposed method.