LMI-Based Approaches To Stability Analysis And Synthesis For Networked Control Systems

Feedback control systems wherein the control loops are closed through a real-time network are called networked control systems (NCSs). With the rapid development of computer applied technology, network technology and control technology, NCSs have received more and more attention, and they have been research focus in control area. Compared with the traditional control systems having point to point structure, advantages of NCSs include low cost, easy installation and maintenance, resource sharing, easy ex-tension, high reliability, etc.Although NCSs may have so many advantages, the introductions of network will also bring about new challenges for the analysis and synthesis of control systems, such as network induced time delay, packet dropout, packet disordering, time-varying sampling interval, signal quantization, bandwidth constraints, etc. These problems have received many scholars’ attention, but how to improve the existing methods or put forward the new research methods to analyze network control systems requires further study and research.In this thesis, the three major issues of induced delay, time-varying sampling, and signal quantization in NCSs are investigated. The network induced delay is a very im-portant factor in the effect of systems performance, and the research of networked control systems with delay has received many scholars’ attention. The thesis gives stability crite-ria for discrete-time NCSs and continuous-time NCSs, respectively, whereas the network induced delays are time-varying. And we have proved in theory that the given results are with less conservative than some existing results.In the most of references concerned with networked control systems, the sampling interval is assumed to be time-invariant. Compared with the time-invariant sampling in-terval, the time-varying sampling control strategy can often make the system get better performance. This thesis studies H∞control problem of networked control systems with time-varying sampling interval, and gives the sufficient conditions of H∞, performance and controller design. The simulation example has shown that the merits of the proposed approach. The control problem of networked control systems with signal quantization is in-vestigated. The control problem of quantized output feedback control for discrete-time networked control system is considered, and the quantized output feedback control strat-egy for the closed-loop systems is presented. In addition, the stabilization problem and H∞control problem of continuous-time network system with the state and the control input signals quantizing are studied, and the conditions of controller design are presented in the terms of LMIs. The simulation example has shown that the effectiveness of the proposed approaches.The specific content arrangement of the thesis is as followings:Chapters1-2summarize the development and main research methods in NCSs liter-ature, give some preliminaries about the considered problem.Chapters3investigates the problem of stability for discrete-time NCSs with time-varying delay. By using Lyapunov functional approach, introducing relax variables tech-nique, and using LMI approach, the new conditions for the stability for discrete-time NCSs are obtained. This result is proved theoretically to be less conservative than some existing ones. The simulations illustrate the advantages of the proposed approaches.Chapters4investigates the problem of the signal quantization on the connection channel between the controller and the controlled plant in feedback control systems, that is, the feedback control problem of quantization. This chapter is concerned with the problem of quantized static output feedback (SOF) for discrete-time networked control systems, whereas the output signals and the input signals are quantized in sensor and con-troller respectively. A novel model of the systems is presented by using sector bounded approach and employing logarithmic quantiser. By using Lyapunov functional approach, together with introducing relaxation variables technique, sufficient conditions for quan-tized NCSs which are asymptotically stable under the SOF controller are presented. The quantized SOF controller design are proposed by using LMI technique and using cone complementary linearization (CCL) algorithm. In addition, the obtained conditions of stability analysis and SOF stabilization for discrete-time NCSs in absence of quantization are proved to be less conservative than some existing results. The simulations further show that the proposed methods’advantages.Chapters5provides new stability conditions for the continuous-time NCSs with time-varying delay or constant delay, respectively. By using new Lyapunov-Krasovskii functionals making use of all the kinds of information on delay related terms, the delay-dependent stability conditions in terms of linear matrix inequalities are presented. It is shown theoretically that the new stability criteria contains less conservative compared to the existing results. The simulations demonstrate effectiveness of the new results.Chapters6focuses on the problem of variable sampling H∞control for net-worked control systems (NCSs) with digital control inputs, where the physical plant is continuous-time signal, and the control inputs are discrete-time signals. The model of the NCSs is presented by input delay approach. Different from the previous chapter, the sampling interval is time-varying, but bounded. By exploiting a Lyapunov-Krasovskii functional which gives full consideration of the upper bound and low bound of sam-pling interval and the bound of network delay, sufficient conditions for H∞performance analysis and H∞controller design of the closed-loop systems are given. By using CCL algorithm, non-convex problem for H∞controller solving is formulated into sequential optimisation problem subject to LMI constraints. The simulations illustrate the proposed approaches are with less conservativeness.Chapter7investigates the quantized control problem of the continuous-time net-worked systems with state feedback. In the systems, the state signals and control input signals are quantized on both sides of sensors and controllers, respectively. Two quan-tization strategy are adopted, i.e., static quantization strategy and dynamic quantization strategy. When the network induced delays and the signals quantization are considered simultaneously, by using the Lyapunov functional approach and the technique of induc-ing relaxation variables, the conditions of stability analysis and controller design under the two quantization strategy are presented in terms of LMIs, respectively. In addition, the given conditions have the merits of less decision variables and less computational amount. And an improved method is proposed to reduce conservativeness of conditions under static quantization strategy. The simulation has shown the effectiveness of the pro-posed method.Chapter8investigates the quantized H∞control problem of continuous-time net-worked control systems (NCSs) on the base of chapter7, where the effects of both network-induced delays and signals quantization exist. The conditions of quantized H∞controller design for the closed-loop NCSs are presented in terms of LMIs by using the Lyapunov functional approach, Jessen inequality method, inducing relax variables tech-nique and sector bound method so on. The simulation illustrates the effectiveness of the proposed method.Finally, the results of the dissertation are summarized and further research topics are pointed out.