The delay phenomenon is prevalent in the real world especially in the industrial processes owing to the actions from transmission and so on. The research on the time-delay systems is the key issue in the control theory and control engineering for the great importance in the practical and theoretical application. Delay is frequently one of the important sources of performance degradation and instability in many dynamic systems, in addition, the existence of delay makes the system analysis and synthesis more complicated and difficult. Thus, it is of a great importance to study the stability analysis and synthesis problems of time-delay systems for the complication and the practical application.This thesis investigates the stability problems of linear time-delay systems and the design of controller for the networked control systems. Recently, the delay decomposition approach is very effective to study time-delay systems. Based on the delay decomposition approach and Lyapunov-Krasovskii functional, using an integral inequality to bound the cross term in the derivative of Lyapunov-Krasovskii functional, this thesis studies the stability of linear time-delay systems and the controller design method of networked control systems by linear matrix inequalities (LMIs). The main contents and novelty of this thesis are outlined as follows,1. The background of the research on stability of time-delay systems, the survey of recent research, and the main work of the thesis are stated. Then, the knowledge of preparation of this thesis as well as the important lemmas are introduced.2. The equivalence of a serial of stability criteria for time-delay systems with constant delay is proved, the comparison of the numbers of the variables involved in the results is given. Based on the delay decomposition approach, a delay-dependent stability criterion with the simple structure and less numbers of variables is proposed, and the given stability criterion is theoretically proved to be a mathematically least complex and computationally most efficient one, the problem that the efficiency of most of the existing stability criteria can only be proved from numerical examples is handled.3. An efficient stability criterion is proposed for linear systems with interval time-varying time-delay, and the given stability criterion is theoretically proved to be a mathematically least complex and computationally most efficient one. Based on the delay decomposition approach and a Lyapunov-Krasovskii functional candidate, which makes use of the information of the lower, upper bounds and the middle point of the time-delay interval, simultaneously, a less conservative stability condition is proposed in terms of a linear matrix inequality, the shortcoming of the existing delay decomposition approach which can not be used in time-varying time-delay systems is overcome.4. This thesis establishes the networked control systems (NCSs) model with both the network-induced delays and data packet dropouts, the sufficient condition of the existing of the controller is given in terms of linear matrix inequalities, meanwhile, the maximum allowable network-induced time-delay is calculated, two algorithms based on linear matrix inequality are proposed to solve the matrix inequality, and comparisons of the advantages and disadvantages between two algorithms are given.5. We sum up all the thesis and prospects of the time-delay systems studies. |