Stability Analysis And Synthesis Of Discrete Time-delay Networked Control Systems

In recent years,Networked Control Systems(NCSs)have attracted much attention for their low cost,easy maintenance,convenient installation,and high flexibility.NCSs have been widely used in aerospace,smart grid,fault detection systems,and robotics.However,it is worth noting that,different from the study of a traditional control system,due to the introduction of the communication network in the feedback loop,some new thorny problems have appeared in the research of NCSs,such as network induced delay and packet dropout.This may cause performance degradation and even make the system unstable.In the past few decades,scholars at home and abroad have conducted in-depth research on these issues and achieved rich research results,However,for time-delay NCSs,how to obtain less conservative stability criteria and optimal controller design is still worth further research.For this reason,this article mainly studies the stability analysis and controller design of the discrete time-varying NCSs and the networked Markov jump system with distributed delay.The main contents of this thesis are as follows:1.For the NCSs,first consider the time-varying delay in the system,design a controller that contains the system time delay information,and finally obtain the closed-loop statespace equation of the system,and then construct the Lyapunov-Krasovskii functionals(LKF)that contains the system time delay information.Two new summation inequalities are used to define the double-difference summation term in LKF.The conditions for the existence of system stability are given in the form of linear matrix inequalities(LMI)and based on this,the design scheme of the system controller is given.Finally,through two numerical examples,it is verified that the stability criterion given is less conservative and the effectiveness of the robust control method,which can still maintain a certain robust performance under external disturbances.2.For the NCSs where the controlled object is a Markov jump system,first of all,consider that the delay caused by the network obeys the probability distribution during the data transmission process of the system.In the case of the distributed delay of the system,a controller that contains the system time delay information is designed,and finally,obtain the closed-loop state-space equation of the system under the action of the controller.Then,by constructing the LKF containing the system time delay information,combining with the Lyapunov stability theory and a new generalized summation inequality.The conditions for the existence of system stability are given in the form of LMI.Under the condition of system stability,the comprehensive design problem of the system controller under the given robust performance index is studied,and the design scheme of the system controller is given in the form of LMI.And through two numerical examples,It is verified that the given stability criterion has wider applicability and the effectiveness of the robust control method,and it can still maintain a certain robust performance under external disturbances.Finally,the conclusions obtained in this paper are applied to the inverted pendulum system,which proves its reliability.