Stability Of Multi-rate Networked Control System With Both Packet-dropout And Time-delay

For multi-rate networked control system (NCS), we mean the sampling period ofthe nodes in the system are not the same. That is to say, there is more than onesampling rates in NCSs. Compared with the single-rate control system, the multi-ratearchitecture design makes for increasing stability and reliability of NCS, which is theinevitable outcome of the development of NCS. The majority of previous NCStheories all under the single-rate assumption, but can not be directly used formulti-rate NCS. It is necessary to study the case of multi-rate.Firstly, the model of multi-rate NCS with both time-delay and packet-dropout iscarried out in this paper. Base on approaches of switched systems and communicatesequence, the sufficient conditions of controllability and observability are given.Secondly, in terms of Markovian Packet-dropout theory, a new approach isproposed to convert the multi-rate NCS into a non-uniform sampling system. Themerit of the proposed method lies in its much less conservatism, which is byguaranteeing the Lyapunov function deceases at each sampling step. In the light offree-weighting matrices and linear matrix inequalities (LMIs), sate feedbackcontroller is designed, which can render the multi-rate networked control systemsexponentially mean square stable.And then, aH guaranteed cost controller is designed, the cost function valueless than a bound. The design problems of the optimal guaranteed cost controllersconvex optimization problems with LMIs constraints.Lastly, this paper studied the tracking control for multi-rate NCS. Combined withthe reference input model, we designed the structure and model of the closed-looptracking control system. The proposed method can guarantee the asymptotic trackingof the prescribed reference outputs, when reference inputs are in mean-square sense.