The Absolute Stability And Control For Some Classes Of Systems With Time Delays

In the analysis and synthesis of control systems, the research of absolute stability for Lurie indirect control systems is very important for the analysis and design of nonlinear control systems, and set store by scholars of the domestic and overseas. In the application, because of large-lag linds and transmission process etc. can lead to the delay phenomena. Systems stability and performance are always dominated by the delay phenomena. So the disquisition of the absolute stability for Lurie indirect control sytem with time-delays seems more important. On the other hand, almost of all systems may suffer uncertainties for the practical industrial process, such as unmodeled dynamics, structured parametric uncertainties, change of the operating environment, model reduction and linearization approximations and external disturbances uncertainties, etc. Therefore, it is found that the problems of robust control and filtering for uncertain systems with time-delay.Based on Lyapunov stability theory, matrix theory, Razumikhin technique , vector inequality, Riccati inequality and linear matix inequality are adopted in this thesis. The absolute stability for Lurie indirect control sysyerms, the designing of robust H_∞controllers for uncertain systems and H_∞filtering for a class of neutral delay differential systems are studied. The main contents are as follows: 1. The absolute stability for two classes of Lurie indirect control syterms are concerned in this thesis. Using Razumikhin technique and vector inequality methed ,and through establishing proper Lyapunov function , the sufficient conditions of the absolute stability for two classes of Lurie type indirect control systems are presented. More better condition for the absolute stability of the systems is derived by optimizing the free parameter in stability criteria. And, some examples are presented to illustrate the effectiveness of our results, and some results which are extended and improved.2. For some classes of uncertain systems with time-delay, the problem of analysising and designing H_∞controllers is concerned by LMI approach. A sufficient condition for the closed-loop system which is quadratically stable is presented by solving the Riccati inequality. The designing method of the robust H_∞controllers is given. Finally, some examples are presented to illustrate the effectiveness and superiority of the design method by using Matlab tool box.3. For a class of neutral delay differential systems, the unbiased H_∞filtering is considered. A matrix inequality approach is proposed to design an unbiased H_∞filter, so that the filtering error system is asymptotically stable and the H_∞norm of the transfer function of error system is less than a positive scalarγ. Compared to standard H_∞filtering approach (without the unbiased condition), the unbiased H_∞filtering approach simplifies the designing procedure, and the resulting error system is internal stable, independent of the stability of the original system.