Stability Analysis And Controller Design Of Networked Control Systems With Time-Varying Transmission Delays And Transmission Intervals

Networked control systems (NCSs) are systems in which control loops are closed over a communication network which may be share with other applications. As networked control systems introducing network into a control system bring many advantages over conventional point-to-point control systems, for example:lower cost, simple installation and maintenance, and better system flexibility. However, data exchange via network inevitably results in transmission delay, transmission intervals, packet losses and variable sampling and so on, which will degrade system performance and even lead to closed-loop instability. It is known that packet losses and variable sampling can be equivalently dealt with as time-varying intervals. So how to compensate transmission delays and intervals in a linear networked control system is a fundamental problem. But, in current the related research results of the networked control systems with time-varying transmission delays and transmission intervals is very conservative. This article is based on a random delay method, modeling the distribution of input delay as a dependent nonidentically distributed process, deriving delay-distribution-dependent sufficient conditions for the robust exponential stability of the overall system. The controller design method is formulated as a nonlinear convex optimization problem with linear matrix inequality constraints. The main content of this paper is as follows:Firstly, summarize simply the research background and significance of this topic, the fundemental issues in the research and the present situation of the research. Then, this paper introduces some concepts of uncertainly, robust stabilization, T-S fuzzy model, linear matrix inequality, Lyapunov-krasovskii stability theorem and some commonly used lemma.Secondly, describe the issue of our research in this paper, then model a relevant random delay model, and do stability analysis based on this model. By constructing suitable Lyapunov-Krasovskii functional, and using Jensen integral inequality, schur complement lemma, S-procedure lemma and other two important inequalities; the delay distribution related sufficient conditions of the system robust exponential stability are derived in the form of linear matrix inequalities (LMIs). Then do stabilization analysis of the closed-loop system, involves the processing of nonlinear matrix inequality in the analysis, through the nonlinear matrix inequality into a nonlinear convex optimization problem with constraints of LMIs, the condition of stabilization of the closed-loop system is obtained. Later, the controller design method is given.Finally, we summarize and prospect the full text, point out the contribution of this paper and the next research direction.This paper adopts Lyapunov-Krasovskii function and improved bounded technology of cross-product integral terms, and fully considers the real-time distributed of input delay in analyzing random delay model of systems, this largely reduces the conservative of our results. Numerical examples of later chapters show that the effective of deriving delay-dependent distribution sufficient condition of the system robust exponential stability in this paper.