Stability Analysis And Synthesis For A Class Of Discrete Networked Control Systems

With the increasing demand of industrial control,the control process becomes relatively complicated.The traditional point-to-point centralized control modes are difficult to meet the demand of modern control.Since they are distributed control systems with strong reliability,simple wiring,low maintenance cost and so on,the networked control systems have solved the problem of traditional control system limited by geographical location and have been widely used in various control fields.As we know,ensuring the stability of the control systems is the premise of the studying a system,but because of the characteristics of the network,the networked control systems can not avoid the emergence of network induced delay,data packet loss and other phenomena which will have some impact on the stability of the system.Therefore,domestic and foreign experts have carried out a large amount of long-term research,and obtained a wealth of research results.Compared with the continuous systems,the experts are not so rich in the study of discrete systems,so the stability analysis and controller design of discrete networked control systems still have much research work.In view of the above reasons,this paper will carry out research work from the following aspects.(1)Based on Lyapunov stability theory,we analyze the stability of a class of linear discrete-time networked control systems.Firstly,based on the network,a closed-loop systems mode is built.Then,we construct a Lyapunov-Krasovskii(L-K)functional with much time delay information and do the differential operation.In addition,the discrete Wirtinger inequality method is used to deal with the corresponding difference summation items.By adding a suitable free matrix combined with convex combination approach,the limitation of cross term inequalities can be avoid and the derivations are simplified,then less conservative stability criteria are obtained.Finally,the validity of the criteria are verified by two examples and corresponding Simulink simulation diagrams.(2)The robust stability of system with parametric uncertainty is considered.Based on the previous chapter,the robust stability of system for norm bounded uncertainties and convex polyhedron uncertainties are discussed,respectively.And the corresponding robust stability conditions and controller design approach are given in the form of Linear matrix inequalities,respectively.Finally,an example is given to show the difference between two kinds of uncertainties in the simulation results and operational complexity.(3)The previous studies are all about the stability of linear systems and the design of controllers.Considering the fact that most of the control systems have nonlinear characteristics,so the method based on Takagi-Sugeno fuzzy model is further studied to deal with the nonlinear networked control systems.In view of the forms of membership functions is different from that of fuzzy controllers in the sampling interval,we construct a L-K functional which is different from that of the previous two chapters,and give sufficient conditions for the system to be stable.Based on this,a fuzzy controller is designed to ensure the system is stable within a certain delay range and the effectiveness of the proposed controller is verified by an example.