| There often exist time-delay phenomena in practice. Strictly speaking, it is usually unavoidable that there exist delays in objective things. It reflects obviously in the actual closed loop control systems with delays such as nuclear systems, vessel stable systems, no-losing deliver circuit systems, long-pipeline feedstock or belt transmission and slow reaction course and complicated on-line analyzing instrument, and so on. These systems all exist time-delay phenomena. Comparing with the process without delays, time-delay phenomena usually cause that the response property of the systems become worse, or even cause vibration and unstable phenomena. Thus, it has an important theoretical and practical significance to study the systems with delays.Generally, the mathematic models of the systems, which are establisd- ed when the actual control systems being synthesized, are only approxim- ates to the objects which are being controlled. It is nearly impossible to completely and exactly establish the mathematic models for the objects which are being controlled. That is, there are various of unavoidable errors in process of establishing models. Now, it is said to be a kind of uncertainty that the gap between the system models and the actual control objects. However, it is still hoped that the actual control systems have certain opposing interference capability. Therefore, it also has an important theoretical and practical significance to study the uncertainty and the parameter disturbance of the system models.In this paper, the problems of the stability and the robust absolute stability for some classes of Lurie type control systems were studied, and the main purpose was to discuss the sufficient conditions for judging the stability and the robust absolute stability of some classes of delay type and neutral type of Lurie control systems. For one thing, by utilizing the Lyapunov stability analytic method and the corresponding knowledge of matrix theory, a class of Lurie control systems with multiple delays and nonlinear executives had been extended to some different Lurie type control systems with time-delay controllers or with time-varying delays and time-varying coefficients; for another, some known results were generalized, extended and improved by the Schur lemma and the S-procedure method and the combination of essential matrix theory and corresponding inequality techniques. The main contents of this paper are :Firstly, the problem of the absolute stability for a class of Lurie control system with time-delay controllers was discussed. A sufficient condition for judging the absolute stability of the system was obtained by constructing Lyapunov functional method and by the combination of M-matrix theory and corresponding lemmas. The effectiveness of the result for this control system was illustrated by a concise example.Secondly, the problem of the absolute stability for a class of nonlinear Lurie control system with time-varying delays and time-varying coeffici- ents was investigated. A sufficient condition for judging the absolute stability of the system was deduced by utilizing the similar method and theoretical knowledge as the method mentioned above. Here the time-varying delays can be unbounded functions. The relevant example was given to illustrate the effectiveness of the result.Thirdly, the problem of the absolute stability for a class of general nonlinear Lurie control system with delays was studied. Some sufficient conditions for judging the absolute stability of the system under the different assumptions were obtained by using the similar method as the method mentioned above.Fourth, the problem of the stability for a class of neutral Lurie system with delays in control was discussed. By constructing appropriate Lyapunov functional and the similar method and theoretical knowledge as the method mentioned above, a sufficient condition of judging the asymptotically stable for the system was given. At the same time, the relevant example was given to illustrate the correctness of the result.Fifth, the general nonlinear structure form of the above-mentioned neutral Lurie control system with delays was discussed and a sufficient condition was obtained.Sixth, the problem of the delay-dependent robust absolute stability for a class of neutral type Lurie control system with uncertainty was studied. With the help of the Schur lemma and the S-procedure method, by the combination of essential matrix theory and the relevant inequalities techniques, and by constructing appropriate Lyapunov functional, some delay-dependent suffici- ent conditions for the neutral system with uncertainty were obtained. And the obtained sufficient conditions based on equivalent descriptor form of the original system were expressed in terms of matrix inequalities. Thus, the delay-independent criteria were improved. |
