Stability Analysis Of Time-delay Systems And The Applications In Networked Control Systems

Time-delay is phenomenon encountered widely in life and industrial production. The existence of time-delay may lead to unstable, even make the whole systems breakdown. Therefore, the study of time-delay systems has attracted the close attention of many scholars, which has been one of the hot issue in control field and control engineering.In this paper, we discusses the problem of the stability of constant time-delay system, neutral time-varying delay system based on Lyapunov stability theory, Wirtinger inequality, Jensen inequality and convex combination, then, we do research on the wireless sensor networks(WSNs) measurement and control systems in greenhouse by employing time-delay systems approach. The main research work on this paper are as follows:1) The problem for a class of constant time-delay systems is studied. Based on Lyapunov stability theory, we construct a suitable Lyapunov-Krasovski functional and deal with the integral term in functional derivative through the Wirtinger inequality and obtain a new stability criterion. On the basis of this, we present the design of state feedback controller and output feedback controller. Finally, numerical examples and simulink model are given to show the feasibility and the effectiveness of the proposed method in this paper.2)The problem of neutral systems with time-varying delay is investigated. By employing augmented Lyapunov-Krasovski functional combined with reciprocally convex combination technique, we obtained a novel stability criterion, which can make the systems asymptotically, What’s more, we analyzed the neutral systems with constant time-delay. Finally, numerical examples demonstrate the effectiveness of the proposed method.3)The problem for a class of WSN measurement and control system in greenhouse is addressed. By using time-delay theory and combing the characteristics of greenhouse WSN measurement and control system with time-delay theory, taking temperature and humidity as the research object, we established the mathematic model. Then, we record the single control circuit of temperature and humidity by incorporating the decoupling technique, the maximum allowed time-delay is analyzed. By building a new Lyapunov functional with triple-integral terms, we get the maximum time-delay in WSN measure and control systems in greenhouse. Finally, numerical example is provided to illustrate the feasibility of the proposed method, which can provide theoretical evidence to the practical application.