System With Delay

Time-delay is common and inevitable in nature, and often makes the system property decline or even causes instability. The mathematical models of time-delay systems are infinite-dimensional functional differential equations, while those of delay-free systems are ordinary differential equations, and so the study of time-delay systems is much more difficult than that of delay-free systems. Therefore, the analysis and synthesis for time-delay systems have great theoretical and practical significance.Even in today's advanced technology, time-delay, as an essential feature of systems, can not be completely eliminated. The performances of controlled objects are more complex because of the progress of science and the development of productive forces, and it is more difficult to get precise mathematical models. So the system models are often uncertain, making the analysis and control of time-delay systems become more and more complex and difficult.In this thesis, the stability of the nominal and uncertain time-delay systems will be studied.It is mainly based on Lyapunov stability theory. The techniques used include the free weighting matrix method, the convex combination technique, Leibniz-Newton formula, and the linear matrix inequality. Stability criteria are given in terms of LMIs, and numerical examples are given to illustrate the effectiveness and the merits of the results.1. The stability of the nominal time-delay systems is studied by constructing a new Lyapunov functional. The derivation process adopts methods such as the segmentation of time-delay interval, the free weighting matrix and the convex combination technique. Delay-dependent and delay-independent stability criteria are given in terms of LMIs. Finally, numerical examples are given to show the less conservativeness of the results.2. The robust stability of uncertain time-delay systems is also studied. The uncertainty is assumed to be of the form of norm-bounded perturbations. By extending the results for delay-free systems, delay-dependent and delay-independent stability criteria are given in terms of LMIs. Numerical examples are also given to show the less conservativeness of the results.