Stability Analysis For Systems With Two Additive Time-varying Delay Components

It is known that the phenomena of time delay occur in many practical systems, such asbiological systems，neural networks, automatic systems and communication systems. Time delaysmay be produced by many reasons, e.g., the ageing of component and mechanical wear leads to themeasurement and signal transmission. The existence of time delay causes instability, even poorperformance. With the advancement of technology and the development of social, the systemsbecome more complex, and the requirements of the system control are also increasing. The existenceof time delay makes it more difficult and complicated to analyze and integrate the systems. Hence,much attention is received in stability analysis of the systems.Based on the analysis of literature at home and abroad, the stability of several types of timedelay systems is investigated, and some delay-dependent stability criteria are obtained. In Chapter1,the introduction of the thesis is given, including the research background, the review of time-delaysystems and some common research methods. In Chapter2, the Lyapunov stability theory, relatedlemmas and related symbols are given. In Chapter3, the stability problem of linear time-varyingdelay systems is discussed. Based on the delay-dividing approach, the delay interval is partitionedinto two subintervals. By using integral inequalities, some delay-dependent stability criteria areobtained. In Chapter4, the stability problem of time delay systems with two additive time-varyingdelay components is studied. Reciprocally convex method is used for estimating the upper bound ofthe derivate of the Lyapunov functional. In Chapter5, the stability problem of neutral delay systemswith two additive time-varying delay components is studied. By constructing a new Lyapunovfunctional and combining with delay-dividing approach and inequality method, the stabilityconditions are given. In chapter6, the stability problem of neural networks is considered. In Chapter7, the problem of H performance analysis is concerned. Considering the network control systemthat includes the time delay and data packet dropouts, the state feedback controller is designed. Theconditions of the existence of controller and the method for solving the state feedback gain areproposed.