Time Delay Control System Of Research

Time-delay is widespread in various systems, and has a direct impact on the system dynamics. Meanwhile, uncertainty is inevitable because of the change of running environment, simplification of model, aging of electrical elements and so on. It is well-known that the existence of time-delay and uncertainty in a system may cause instability or bad system performance. Therefore, the analysis and control problems for uncertain time-delay systems have important significance both theoretically and practically. This paper deals with the problem of reachable set estimation for time-delay control systems subject to bounded peak disturbances. A delay-dependent criterion is presented based on appropriately chosen Lyapunov-Krasovskii functional combined with the modified integral inequality. The conditions bounding the reachable set are expressed in terms of linear matrix inequalities. Finally, we show the usefulness of our result by some numerical examples. The main contents of this paper are as follows:(1) The problem of reachable set bounding for linear time-delay control system with bounded peak disturbances is studied by using appropriate Lyapunov-Krasovskii functional. The conditions are derived based on the linear matrix inequalities technique. Delay-independent and delay-dependent state feedback controllers are constructed to obtain a set as small as possible bounding the reachable set. Two examples are given to illustrate the theoretical results.(2) The problem of reachable set estimation for uncertain systems subject to both state time delay and control input delay is also studied. The uncertainties satisfy norm-bounded constraints. We obtain a sufficient condition for state feedback controller design which leads to the reachable set as small as possible. Furthermore, an optimization problem with LMI constraints is established. Numerical examples are given to illustrate the effectiveness of the present results.