Stability And Stabilization Research Of Networked Control Systems With Input Delays

Networked control systems (NCS) is a control system in which the control loop is closed over a communication network. Due to the control system are connected to the network, as opposed to traditional control systems where components are usually con-nected via point-to-point wiring, the framework of NCS has the flexibility, can share re-sources, low cost, and simple installation and maintenance. The introduction of network has brought some advantages, but can’t avoid exposed some problems. For example, common existence network time delay, packet loss, time-varying sampling, the commu-nication limited in the network. As a result of the existence of these problems, often de-grade the performance of the system and even cause instability.In this paper, we mainly aims at research the problem of the short time delay, separ-ately by two ideas were analyzed. The first idea is the system as a linear to consider. Be-cause every system is a nonlinear system, just for the convenience of analysis, as a linear to deal with it. The second idea is the basis of the nonlinear systems, by T-S fuzzy model to analyze, with some simple weighted sum of linear system to express a nonlinear sys-tem. Through analyzing the two train of thought for a short time delay, introduced a con-servative in the process of analysis, in order to reduce the conservative of system, we use a special method to deal with. Due to the short time delay express the network induced delay is less than one sampling period, and the next sampling point in transmission inter-val, we will take the sample point as the switch point, construct two different Lyapunov functional to analysis, but the two Lyapunov functional exists coupling problem. For the coupling problem, we judged by impulsive effects. In the size of the delay encountered in the time delay problem, we can assume that the range of the time delay, consider the range of transmission delay and input delay, respectively, and based on the problems of convexity, to analyze the maximum and minimum value, respectively. Finally, combined with linear matrix inequality (LMI) to judge the stability of the system. In the stability analysis we make full use of the Jensen inequality, free weight matrix inequalities, Schur complement lemma, etc. For stabilization analysis, the controller is variable, the basis on stability, we will through the Schur complement theorem to nonlinear matrix inequality transform into LMI, finally we use parameter adjusting factor method get control gain.The chapter 1 and the chapter 2 introduce research background and significance of NCS, the overview of NCS as well as some this article involves the knowledge points.The chapter 3 presents new stability criteria for an NCS with time-varying transmis-sion delays and intervals based on a discontinuous Lyapunov functional approach. Here, the evolution of transmission delays is additionally taken into account. The accumulating transmission delays are described as the potential form of input delays, and the impulsive effects of input delays are more fully revealed. A new discontinuous Lyapunov functional is proposed to appropriately consider the impulsive effects of input delays and feedback signals as well as the time derivative of input delays, which leads to less conservatism in the derived stability criteria. Numerical example is presented to substantiate the advent-age of our proposed approach.In the chapter 4, based on the T-S fuzzy model and input delay impulsive method to analyze the nonlinear system for NCS with transmission delay and transmission interval. The first constructing a novel Lyapunov functional to obtained the sufficient condition of stability for NCS. Then to analysis the fuzzy controller, by the parameter adjusting factor method obtained the fuzzy control gain. A nonlinear mass-spring system example is presented to substantiate the advantage of our proposed approach.