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

Time-delay phenomenon has received much attention due to its profound practical background and time-delays are often the source of instability and degradation in control performance. By using the existing stability analysis methods, sufficient conditions are often obtained and reducing the conservatism is important for the practicality and industrialization of the control algorithm. However, there are few systematical discussions about the conservatism of the stability criteria.For nominal linear time-delay systems, the equivalence of stability criteria is defined and the conservatism of the stability criteria is deeply analyzed. Based on Lyapunov-Krasovskii stability theory, the stability analysis of singular time-delay systems,Lur'e time-delay systems,time-delay systems with Markovian parameters,delayed cellular neural networks systems are proposed in this dissertation and the sufficient conditions for the existence of the controller are derived with respect to the performance. Some characteristics of network control systems are deeply studied, such as: time-delay, packet-drop out, quantization and the state feedback controller is designed which guarantees the closed-loop system stable. Finally, state feedback control algorithm developed in this dissertation is applied in the process of a distillation column control system simulation. The main contents of this dissertation are outlined as follows:(1) For linear time-delay systems, some stability analysis methods are proved theoretically to be equivalent, which is different from the regular practice that most of the criteria are compared via numerical examples. Furthermore, a method is given to judge if a slack variable is redundant. Finally, we concluded that the slack variable method is more suitable to deal with polytopic uncertain systems.(2) For singular time-delay systems,Lur'e time-delay systems,time-delay systems with Markovian parameters and delayed cellular neural networks systems, the integral inequality method is used to derive the delay-dependent stability criteria, based on which the controller design problem are formulated as the solvability of some iterative linear matrix inequalities. It is proved theoretically that the results obtained in this dissertation are less conservative than some existing results. The stability criteria obtained for singular time-delay systems also guarantee the system regular and impulse free. The controller is designed which satisfied the proposed guaranteed cost and dissipative performance.(3) For the networked control systems with time-varying time-delay, the integral inequality method is used to derive the stability criteria. The criteria are independent of the delay derivative bound, e.g., the delay considered here is allowed to be fast-varying, which is more suitable for networked control systems. Furthermore, the analysis is focused on how the packet dropping affects state estimation and what we can do to compensate this unreliability. The H_∞controller is obtained which allows a maximum allowable delay size for a fixed disturbance rejection performance value. Finally, the quantized feedback controller is designed which guarantees the Lyapunov stability of closed-loop systems. Besides, the relationship among the packet-dropping rate, time delay and the average data rate is also obtained in the meanwhile.(4) The state feedback control strategy developed in this dissertation is applied for the distillation column control system simulation. Simulation results demonstrate the validity and excellent performance of this method. This part constitutes an attempt of applying the Lyapunov stability idea to practical engineering problems.