Research On Robust Control For Uncertain Linear Time-Delay Systems

In control system design process, using a mathematical model to fully reflect the actual controlled object is almost impossible, because the complexity of the controlled object model makes a gap between the actual object and the model we get. The gap can be regarded as system model uncertainty. On the other hand, the existing of delay phenomenon in many practical systems will often result in system instability or poor performance of the dynamic response of the system. Therefore, the study of uncertain systems with time-delay has important theoretical and practical significance, which is also the current research focus on the field of control.Many control experts have been studying the systems with the coexistence of delay and uncertainty phenomena and got good results, but in many practical systems, besides the delay and uncertainty phenomena, the nonlinear factors should also be taken into consideration, the most common factor is the nonlinear saturation. In this paper, by applying a new Lyapunov functional, using convex combination to deal with saturation functions, examples verify that the results obtained are less conservative. The main results of the thesis are as follows:1. Based on LMI the interval time-delay systems are studied, both the stability for the certain interval delay system, and the robust stability for uncertain interval delay systems are studied, sufficient conditions of stabilization and robust stabilization for systems and the state feedback controller are obtained, numerical examples are given by using the LMI toolbox in MATLAB, which show that the theorems are effective and reasonable.2. For a class of uncertain systems with time-delay containing saturating actuator, the convex combination is used to deal with saturation functions and the integral term is handled through the use of integral inequality; sufficient conditions of asymptotic stability of closed-loop system are obtained based on LMI, a algorithm for estimating of the domain of attraction is also obtained; memoryless feedback controller is designed; By using the LMI toolbox in MATLAB, numerical examples is given to show that the theorems are effective and reasonable.